Weeks Between Easters

Weeks Between Easters:

This began with Eric Weisstein's statement that "consecutive Easters are always separated by 350, 357, 378, or 385 days." I thought these numbers worthy of recognition in Neil Sloane's On-Line Encyclopedia of Integer Sequences and so, by way of extending the concept to non-consecutive Easters (and dividing by seven), I begat A134691: Possible number of weeks between two (Gregorian calendar) Easters.

After some initial experimentation, it became obvious to me that in order to not exclude some rare occurrences, I would need to search all 5700000 possibilities (5700000 years is the length of the Gregorian Easter cycle) for each year-separation calculation. That is to say, only after checking the number of weeks separating two Easters one year apart for all 5700000 years beginning with 1583 (the first possible Easter year of the Gregorian calendar) could I be certain that the only possible weeks-apart were 50, 51, 54, 55. At least by using this method, I could simultaneously extract the frequency of occurrence of each weeks-apart out of the total 5700000 and grab an explicit example for each:

YEARS WEEKS FREQUENCY EARLIEST EXAMPLE

0 0 5700000 1583 - 1583

1 50 1403218 1585 - 1586

1 51 2197599 1583 - 1584

1 54 281764 1608 - 1609

1 55 1817419 1584 - 1585

2 101 1162499 1585 - 1587

2 102 339135 1609 - 1611

2 105 2207465 1584 - 1586

2 106 1990901 1583 - 1585

3 155 26760 2316 - 2319

3 156 4582081 1583 - 1586

3 157 493610 1602 - 1605

3 160 419345 1587 - 1590

3 161 178204 1598 - 1601

4 206 910534 1585 - 1589

4 207 2092734 1583 - 1587

4 210 129394 1605 - 1609

4 211 2567338 1584 - 1588

5 257 605600 1590 - 1595

5 258 298485 1609 - 1614

5 261 2119310 1584 - 1589

5 262 2676605 1583 - 1588

6 311 1152 7996 - 8002

6 312 3708061 1583 - 1589

6 313 795689 1599 - 1605

6 316 699527 1584 - 1590

6 317 495571 1595 - 1601

7 362 518740 1585 - 1592

7 363 1886979 1590 - 1597

7 366 67902 1744 - 1751

7 367 3034611 1583 - 1590

7 368 191768 1598 - 1605

8 413 160247 1590 - 1598

8 414 146289 1609 - 1617

8 417 1919609 1584 - 1592

8 418 3473855 1583 - 1591

9 468 2886241 1583 - 1592

9 469 1021112 1596 - 1605

9 472 878597 1584 - 1593

9 473 914050 1592 - 1601

10 518 233955 1585 - 1595

10 519 1567978 1590 - 1600

10 520 6237 5739 - 5749

10 522 11762 2096 - 2106

10 523 3390408 1583 - 1593

10 524 489660 1595 - 1605

11 573 1406643 1584 - 1595

11 574 4002344 1583 - 1594

11 577 28159 1970 - 1981

11 578 262854 1598 - 1609

12 624 2162815 1583 - 1595

12 625 1146989 1593 - 1605

12 628 956969 1584 - 1596

12 629 1433227 1589 - 1601

13 674 67487 1585 - 1598

13 675 1113020 1590 - 1603

13 676 30114 1981 - 1994

13 678 688 6098 - 6111

13 679 3555396 1583 - 1596

13 680 933295 1592 - 1605

14 729 840077 1584 - 1598

14 730 3967936 1583 - 1597

14 731 3425 5739 - 5753

14 733 15162 2092 - 2106

14 734 811334 1587 - 1601

14 735 62066 1598 - 1612

15 780 1540270 1583 - 1598

15 781 1171985 1590 - 1605

15 784 934460 1584 - 1599

15 785 2053285 1586 - 1601

16 830 1536 4292 - 4308

16 831 557985 1590 - 1606

16 832 53551 1609 - 1625

16 835 3598655 1583 - 1599

16 836 1488273 1589 - 1605

17 885 406058 1585 - 1602

17 886 3780871 1583 - 1600

17 887 26960 2299 - 2316

17 889 1376 2089 - 2106

17 890 1248955 1584 - 1601

17 891 235780 1595 - 1612

18 936 1018293 1585 - 1603

18 937 1096413 1590 - 1608

18 940 811383 1584 - 1602

18 941 2773911 1583 - 1601

19 987 13889 1685 - 1704

19 988 4522 2296 - 2315

19 991 3499097 1583 - 1602

19 992 2179604 1586 - 1605

19 995 1672 3583 - 3602

19 996 1216 2391 - 2410

20 1041 53244 1798 - 1818

20 1042 3529540 1583 - 1603

20 1043 33556 1609 - 1629

20 1045 96 31083 - 31103

20 1046 1563420 1584 - 1604

20 1047 520144 1592 - 1612

21 1092 591502 1585 - 1606

21 1093 925655 1590 - 1611

21 1096 593120 1588 - 1609

21 1097 3589723 1583 - 1604

22 1147 2682986 1584 - 1606

22 1148 2434988 1583 - 1605

22 1151 186618 1587 - 1609

22 1152 395408 1598 - 1620

23 1197 29404 2096 - 2119

23 1198 2715210 1583 - 1606

23 1199 274177 1602 - 1625

23 1201 128 17992 - 18015

23 1202 1780312 1584 - 1607

23 1203 900769 1589 - 1612

24 1248 262731 1612 - 1636

24 1249 656877 1590 - 1614

24 1252 276837 1585 - 1609

24 1253 4503555 1583 - 1607

25 1303 1986031 1585 - 1610

25 1304 2534394 1583 - 1608

25 1307 238519 1584 - 1609

25 1308 941056 1587 - 1612

26 1353 3752 4292 - 4318

26 1354 2005213 1585 - 1611

26 1355 412277 1599 - 1625

26 1358 1896815 1583 - 1609

26 1359 1381943 1586 - 1612

27 1404 44481 1666 - 1693

27 1405 277578 1590 - 1617

27 1408 130456 1724 - 1751

27 1409 4967062 1583 - 1610

27 1410 280423 1598 - 1625

28 1459 1390171 1585 - 1613

28 1460 2532705 1583 - 1611

28 1463 189325 1625 - 1653

28 1464 1587799 1584 - 1612

29 1510 1352376 1585 - 1614

29 1511 471317 1596 - 1625

29 1514 1912102 1584 - 1613

29 1515 1964205 1583 - 1612

30 1564 18320 2089 - 2119

30 1565 4714803 1583 - 1613

30 1566 691387 1595 - 1625

30 1569 198017 1617 - 1647

30 1570 77473 1598 - 1628

31 1615 894980 1585 - 1616

31 1616 2430347 1583 - 1614

31 1619 105675 1720 - 1751

31 1620 2202785 1584 - 1615

31 1621 66213 1598 - 1629

32 1666 792831 1585 - 1617

32 1667 433313 1593 - 1625

32 1670 1826593 1584 - 1616

32 1671 2647263 1583 - 1615

33 1721 3811173 1583 - 1616

33 1722 1015788 1592 - 1625

33 1725 493233 1587 - 1620

33 1726 379806 1595 - 1628

34 1771 503104 1585 - 1619

34 1772 2222126 1583 - 1617

34 1773 2548 5739 - 5773

34 1775 33651 2072 - 2106

34 1776 2693752 1584 - 1618

34 1777 244819 1595 - 1629

35 1822 334199 1601 - 1636

35 1823 294396 1590 - 1625

35 1826 1640171 1584 - 1619

35 1827 3431234 1583 - 1618

36 1877 2984555 1583 - 1619

36 1878 1244857 1589 - 1625

36 1881 674797 1584 - 1620

36 1882 795791 1592 - 1628

37 1927 220378 1585 - 1622

37 1928 1896258 1588 - 1625

37 1929 13593 2299 - 2336

37 1931 3088 2069 - 2106

37 1932 3001144 1583 - 1620

37 1933 565539 1592 - 1629

38 1978 12920 1666 - 1704

38 1979 23902 1685 - 1723

38 1982 1315180 1584 - 1622

38 1983 4342222 1583 - 1621

38 1986 1216 7971 - 8009

38 1987 4560 2372 - 2410

39 2033 2255869 1583 - 1622

39 2034 1375994 1586 - 1625

39 2037 758429 1584 - 1623

39 2038 1309708 1589 - 1628

40 2083 37184 1778 - 1818

40 2084 1466766 1585 - 1625

40 2085 28730 1609 - 1649

40 2087 368 12691 - 12731

40 2088 3157410 1583 - 1623

40 2089 1009542 1589 - 1629

41 2138 724968 1585 - 1626

41 2139 4401728 1583 - 1624

41 2140 6801 5367 - 5408

41 2142 8500 2065 - 2106

41 2143 515598 1587 - 1628

41 2144 42405 1598 - 1639

42 2189 1621859 1585 - 1627

42 2190 1412455 1583 - 1625

42 2193 747385 1584 - 1626

42 2194 1918301 1586 - 1628

43 2239 8514 4292 - 4335

43 2240 825975 1590 - 1633

43 2241 100642 1609 - 1652

43 2243 280 12688 - 12731

43 2244 3210663 1583 - 1626

43 2245 1553926 1586 - 1629

44 2294 268312 1629 - 1673

44 2295 4249074 1583 - 1627

44 2296 18562 1981 - 2025

44 2298 1248 2089 - 2133

44 2299 951014 1584 - 1628

44 2300 211790 1595 - 1639

45 2345 1088839 1585 - 1630

45 2346 1347926 1590 - 1635

45 2349 635351 1605 - 1650

45 2350 2627884 1583 - 1628

46 2396 254477 1590 - 1636

46 2397 83105 1609 - 1655

46 2400 3154695 1584 - 1630

46 2401 2207723 1583 - 1629

47 2450 104389 1724 - 1771

47 2451 3611564 1583 - 1630

47 2452 222446 1602 - 1649

47 2454 576 12684 - 12731

47 2455 1272660 1584 - 1631

47 2456 488365 1592 - 1639

48 2501 656796 1585 - 1633

48 2502 1182420 1590 - 1638

48 2505 422340 1605 - 1653

48 2506 3438444 1583 - 1631

49 2556 2675324 1584 - 1633

49 2557 2764709 1583 - 1632

49 2560 88794 1723 - 1772

49 2561 171173 1598 - 1647

50 2606 19904 2069 - 2119

50 2607 2915791 1583 - 1633

50 2608 405155 1599 - 1649

50 2611 1493501 1584 - 1634

50 2612 865649 1589 - 1639

51 2657 325461 1585 - 1636

51 2658 916206 1590 - 1641

51 2661 219525 1700 - 1751

51 2662 4127904 1583 - 1634

51 2663 110904 1598 - 1649

52 2712 1962392 1584 - 1636

52 2713 2880092 1583 - 1635

52 2716 156672 1625 - 1677

52 2717 700844 1587 - 1639

53 2763 2191856 1583 - 1636

53 2764 551445 1596 - 1649

53 2767 1612190 1584 - 1637

53 2768 1344509 1586 - 1639

54 2813 96707 1639 - 1693

54 2814 545620 1590 - 1644

54 2815 1791 5739 - 5793

54 2817 70324 2052 - 2106

54 2818 4609346 1583 - 1637

54 2819 376212 1595 - 1649

55 2868 1363884 1585 - 1640

55 2869 2881051 1583 - 1638

55 2872 118344 1720 - 1775

55 2873 1328503 1584 - 1639

55 2874 8218 3401 - 3456

56 2919 1529055 1585 - 1641

56 2920 616697 1593 - 1649

56 2923 1629937 1584 - 1640

56 2924 1924311 1583 - 1639

57 2970 52972 1647 - 1704

57 2971 2261 4995 - 5052

57 2974 4783858 1583 - 1640

57 2975 852245 1592 - 1649

57 2978 7144 2372 - 2429

57 2979 1520 2353 - 2410

58 3024 863191 1585 - 1643

58 3025 2784195 1583 - 1641

58 3028 61207 1744 - 1802

58 3029 1895965 1584 - 1642

58 3030 95442 1598 - 1656

59 3075 961389 1585 - 1644

59 3076 586814 1590 - 1649

59 3079 1552549 1584 - 1643

59 3080 2599248 1583 - 1642

60 3130 3890361 1583 - 1643

60 3131 1258659 1589 - 1649

60 3134 308559 1587 - 1647

60 3135 242421 1598 - 1658

61 3180 463325 1585 - 1646

61 3181 2580700 1583 - 1644

61 3182 5812 5367 - 5428

61 3184 21920 1744 - 1805

61 3185 2332712 1584 - 1645

61 3186 295531 1595 - 1656

62 3231 491300 1601 - 1663

62 3232 459354 1590 - 1652

62 3235 1377584 1584 - 1646

62 3236 3371762 1583 - 1645

63 3286 3052448 1583 - 1646

63 3287 1499023 1586 - 1649

63 3290 501418 1584 - 1647

63 3291 647111 1595 - 1658

64 3336 167904 1629 - 1693

64 3337 2269520 1585 - 1649

64 3338 14864 1981 - 2045

64 3340 2016 2069 - 2133

64 3341 2629488 1583 - 1647

64 3342 616208 1592 - 1656

65 3387 130295 1628 - 1693

65 3388 222810 1590 - 1655

65 3391 1093535 1585 - 1650

65 3392 4253360 1583 - 1648

66 3442 2315302 1585 - 1651

66 3443 1638620 1583 - 1649

66 3446 593510 1584 - 1650

66 3447 1152568 1592 - 1658

67 3492 55204 1778 - 1845

67 3493 1693347 1585 - 1652

67 3494 106188 1609 - 1676

67 3496 800 12664 - 12731

67 3497 2788439 1583 - 1650

67 3498 1056022 1589 - 1656

68 3547 587124 1585 - 1653

68 3548 4868432 1583 - 1651

68 3551 3432 2065 - 2133

68 3552 229232 1617 - 1685

68 3553 11780 1598 - 1666

69 3598 1678840 1585 - 1654

69 3599 1677533 1583 - 1652

69 3602 584918 1584 - 1653

69 3603 1758709 1587 - 1656

70 3648 8352 4292 - 4362

70 3649 1086155 1585 - 1655

70 3650 162683 1609 - 1679

70 3653 2845881 1583 - 1653

70 3654 1596929 1586 - 1656

71 3703 235514 1680 - 1751

71 3704 4488222 1583 - 1654

71 3705 134271 1609 - 1680

71 3707 1424 6040 - 6111

71 3708 671624 1587 - 1658

71 3709 168945 1595 - 1666

72 3754 1143565 1585 - 1657

72 3755 1615259 1583 - 1655

72 3758 475139 1605 - 1677

72 3759 2466037 1584 - 1656

73 3805 502995 1590 - 1663

73 3806 156646 1609 - 1682

73 3809 2800691 1584 - 1657

73 3810 2239668 1583 - 1656

74 3859 56792 1744 - 1818

74 3860 3877561 1583 - 1657

74 3861 326105 1602 - 1676

74 3864 997523 1584 - 1658

74 3865 442019 1592 - 1666

75 3910 708849 1585 - 1660

75 3911 1452426 1590 - 1665

75 3914 277367 1676 - 1751

75 3915 3248792 1583 - 1658

75 3916 12566 3401 - 3476

76 3961 42313 1628 - 1704

76 3962 31331 1647 - 1723

76 3965 2611455 1584 - 1660

76 3966 3003349 1583 - 1659

76 3969 4864 2372 - 2448

76 3970 6688 2334 - 2410

77 4015 4104 5452 - 5529

77 4016 3112976 1583 - 1660

77 4017 545829 1599 - 1676

77 4020 1222430 1584 - 1661

77 4021 814661 1589 - 1666

78 4066 369184 1585 - 1663

78 4067 1194542 1590 - 1668

78 4070 140091 1724 - 1802

78 4071 3815504 1583 - 1661

78 4072 180679 1598 - 1676

79 4121 1916776 1584 - 1663

79 4122 3247767 1583 - 1662

79 4125 96802 1723 - 1802

79 4126 438655 1587 - 1666

80 4172 2346495 1583 - 1663

80 4173 718865 1596 - 1676

80 4176 1352065 1584 - 1664

80 4177 1282575 1586 - 1666

81 4222 132370 1612 - 1693

81 4223 828864 1590 - 1671

81 4224 4943 5367 - 5448

81 4226 47964 1724 - 1805

81 4227 4194010 1583 - 1664

81 4228 491849 1595 - 1676

82 4277 1306974 1585 - 1667

82 4278 3260020 1583 - 1665

82 4281 87503 1720 - 1802

82 4282 1019550 1584 - 1666

82 4283 25953 1598 - 1680

83 4328 1672492 1585 - 1668

83 4329 795319 1593 - 1676

83 4332 1381014 1584 - 1667

83 4333 1851175 1583 - 1666

84 4378 5472 1734 - 1818

84 4379 351430 1590 - 1674

84 4380 11726 1981 - 2065

84 4383 4376114 1583 - 1667

84 4384 955258 1592 - 1676

85 4433 801120 1585 - 1670

85 4434 3165365 1583 - 1668

85 4435 2960 5367 - 5452

85 4437 42516 1720 - 1805

85 4438 1570833 1584 - 1669

85 4439 117206 1595 - 1680

86 4484 1099171 1585 - 1671

86 4485 771091 1590 - 1676

86 4488 1309281 1584 - 1670

86 4489 2520457 1583 - 1669

87 4539 3957163 1583 - 1670

87 4540 1513916 1589 - 1676

87 4543 136271 1723 - 1810

87 4544 92650 1598 - 1685

88 4589 397584 1585 - 1673

88 4590 2967018 1583 - 1671

88 4591 7294 1981 - 2069

88 4593 5200 2045 - 2133

88 4594 2005830 1584 - 1672

88 4595 317074 1592 - 1680

89 4640 626556 1585 - 1674

89 4641 646157 1590 - 1679

89 4644 1136842 1584 - 1673

89 4645 3290445 1583 - 1672

90 4695 3101329 1583 - 1673

90 4696 1772201 1586 - 1676

90 4699 347051 1587 - 1677

90 4700 479419 1595 - 1685

91 4745 153116 1680 - 1771

91 4746 2550979 1583 - 1674

91 4747 70252 1609 - 1700

91 4749 1944 6020 - 6111

91 4750 2272263 1584 - 1675

91 4751 651446 1589 - 1680

92 4796 255194 1601 - 1693

92 4797 419970 1590 - 1682

92 4800 863150 1585 - 1677

92 4801 4161686 1583 - 1675

93 4851 2361505 1585 - 1678

93 4852 1914476 1583 - 1676

93 4855 441821 1584 - 1677

93 4856 982198 1587 - 1680

94 4901 35200 1724 - 1818

94 4902 1982489 1585 - 1679

94 4903 159109 1609 - 1703

94 4906 2435419 1583 - 1677

94 4907 1087783 1586 - 1680

95 4952 16150 1666 - 1761

95 4953 75905 1609 - 1704

95 4956 456684 1656 - 1751

95 4957 5136821 1583 - 1678

95 4960 456 17920 - 18015

95 4961 13984 2315 - 2410

96 5007 1720123 1585 - 1681

96 5008 1958309 1583 - 1679

96 5011 438149 1625 - 1721

96 5012 1583419 1584 - 1680

97 5057 3136 4292 - 4389

97 5058 1337735 1585 - 1682

97 5059 238378 1609 - 1706

97 5062 2499247 1584 - 1681

97 5063 1621504 1583 - 1680

98 5112 174905 1707 - 1805

98 5113 4761022 1583 - 1681

98 5114 244139 1602 - 1700

98 5116 648 5793 - 5891

98 5117 416108 1587 - 1685

98 5118 103178 1598 - 1696

99 5163 1173349 1585 - 1684

99 5164 1907534 1583 - 1682

99 5167 339869 1649 - 1748

99 5168 2279248 1584 - 1683

100 5214 733197 1590 - 1690

100 5215 248503 1609 - 1709

100 5218 2465003 1584 - 1684

100 5219 2253297 1583 - 1683

101 5268 42720 1724 - 1825

101 5269 4046576 1583 - 1684

101 5270 493221 1599 - 1700

101 5273 751166 1584 - 1685

101 5274 366317 1595 - 1696

102 5319 727699 1585 - 1687

102 5320 1755635 1590 - 1692

102 5323 223829 1649 - 1751

102 5324 2909473 1583 - 1685

102 5325 83364 1598 - 1700

103 5370 229624 1590 - 1693

103 5371 154527 1609 - 1712

103 5374 2323522 1584 - 1687

103 5375 2992327 1583 - 1686

104 5425 3254365 1583 - 1687

104 5426 730603 1596 - 1700

104 5429 983763 1584 - 1688

104 5430 731269 1592 - 1696

105 5475 385494 1585 - 1690

105 5476 1497987 1590 - 1695

105 5477 2304 5891 - 5996

105 5479 93704 1700 - 1805

105 5480 3466727 1583 - 1688

105 5481 253784 1595 - 1700

106 5526 288 6597 - 6703

106 5527 576 22498 - 22604

106 5530 1860611 1584 - 1690

106 5531 3624263 1583 - 1689

106 5534 47193 1723 - 1829

106 5535 167069 1704 - 1810

107 5581 2477115 1583 - 1690

107 5582 910304 1593 - 1700

107 5585 1115959 1584 - 1691

107 5586 1196622 1589 - 1696

108 5631 145124 1585 - 1693

108 5632 1137484 1590 - 1698

108 5633 5628 1981 - 2089

108 5635 7408 2025 - 2133

108 5636 3835508 1583 - 1691

108 5637 568848 1592 - 1700

109 5686 1233847 1584 - 1693

109 5687 3653966 1583 - 1692

109 5688 1240 5891 - 6000

109 5690 50838 1720 - 1829

109 5691 739702 1587 - 1696

109 5692 20407 1598 - 1707

110 5737 1801082 1583 - 1693

110 5738 988788 1590 - 1700

110 5741 1146938 1584 - 1694

110 5742 1763192 1586 - 1696

111 5787 26648 1707 - 1818

111 5788 633596 1590 - 1701

111 5789 30443 1609 - 1720

111 5791 2824 5780 - 5891

111 5792 3940462 1583 - 1694

111 5793 1066027 1589 - 1700

112 5842 723464 1585 - 1697

112 5843 3566196 1583 - 1695

112 5844 1844 3344 - 3456

112 5846 11816 1994 - 2106

112 5847 1281228 1584 - 1696

112 5848 115452 1595 - 1707

113 5893 1225657 1585 - 1698

113 5894 966664 1590 - 1703

113 5897 1077309 1584 - 1697

113 5898 2430370 1583 - 1696

114 5944 84885 1590 - 1704

114 5945 21325 1609 - 1723

114 5948 3894551 1583 - 1697

114 5949 1686167 1586 - 1700

114 5952 8512 2315 - 2429

114 5953 4560 2353 - 2467

115 5998 325323 1656 - 1771

115 5999 3351658 1583 - 1698

115 6000 16974 1609 - 1724

115 6002 5888 2336 - 2451

115 6003 1658850 1584 - 1699

115 6004 341307 1592 - 1707

116 6049 745369 1585 - 1701

116 6050 849403 1590 - 1706

116 6053 912543 1605 - 1721

116 6054 3192685 1583 - 1699

117 6104 3130986 1584 - 1701

117 6105 2064603 1583 - 1700

117 6108 211908 1655 - 1772

117 6109 292503 1598 - 1715

118 6154 127252 1700 - 1818

118 6155 2832251 1583 - 1701

118 6156 136903 1602 - 1720

118 6158 1088 5773 - 5891

118 6159 1938945 1584 - 1702

118 6160 663561 1589 - 1707

119 6205 362890 1585 - 1704

119 6206 634333 1590 - 1709

119 6209 649968 1629 - 1748

119 6210 4052809 1583 - 1702

120 6260 2380325 1584 - 1704

120 6261 2217715 1583 - 1703

120 6264 317515 1625 - 1745

120 6265 784445 1587 - 1707

121 6310 28840 1724 - 1845

121 6311 2214307 1583 - 1704

121 6312 255710 1599 - 1720

121 6315 2110835 1584 - 1705

121 6316 1090308 1586 - 1707

122 6361 87024 1639 - 1761

122 6362 312650 1590 - 1712

122 6365 401335 1629 - 1751

122 6366 4778436 1583 - 1705

122 6367 120555 1598 - 1720

123 6416 1730749 1585 - 1708

123 6417 2269742 1583 - 1706

123 6420 322037 1625 - 1748

123 6421 1377472 1584 - 1707

124 6467 1558079 1585 - 1709

124 6468 343229 1596 - 1720

124 6471 2179689 1584 - 1708

124 6472 1619003 1583 - 1707

125 6518 3456 2190 - 2315

125 6519 144 29395 - 29520

125 6521 123728 1680 - 1805

125 6522 5003269 1583 - 1708

125 6523 367928 1595 - 1720

125 6526 168569 1704 - 1829

125 6527 32906 1761 - 1886

126 6572 1181806 1585 - 1711

126 6573 2221136 1583 - 1709

126 6576 252939 1625 - 1751

126 6577 2017106 1584 - 1710

126 6578 27013 1598 - 1724

127 6623 944763 1585 - 1712

127 6624 358996 1593 - 1720

127 6627 2147951 1584 - 1711

127 6628 2248290 1583 - 1710

128 6678 4257395 1583 - 1711

128 6679 647181 1592 - 1720

128 6682 520301 1587 - 1715

128 6683 275123 1598 - 1726

129 6728 735009 1585 - 1714

129 6729 2069456 1583 - 1712

129 6730 928 5891 - 6020

129 6732 131748 1676 - 1805

129 6733 2659708 1584 - 1713

129 6734 103151 1595 - 1724

130 6779 432443 1601 - 1731

130 6780 273767 1590 - 1720

130 6783 2015217 1584 - 1714

130 6784 2978573 1583 - 1713

131 6834 3376778 1583 - 1714

131 6835 930249 1589 - 1720

131 6838 755864 1584 - 1715

131 6839 637109 1595 - 1726

132 6884 387832 1585 - 1717

132 6885 1819178 1588 - 1720

132 6886 834 3344 - 3476

132 6888 15088 1974 - 2106

132 6889 3192606 1583 - 1715

132 6890 284462 1592 - 1724

133 6935 50439 1628 - 1761

133 6936 68406 1590 - 1723

133 6939 1749583 1584 - 1717

133 6940 3821388 1583 - 1716

133 6943 2584 2315 - 2448

133 6944 7600 2334 - 2467

134 6990 2594535 1583 - 1717

134 6991 1114943 1586 - 1720

134 6994 893053 1584 - 1718

134 6995 1097469 1592 - 1726

135 7040 148715 1680 - 1815

135 7041 1447524 1585 - 1720

135 7042 14056 1609 - 1744

135 7044 12536 2316 - 2451

135 7045 3402544 1583 - 1718

135 7046 674625 1589 - 1724

136 7095 1139314 1585 - 1721

136 7096 4071798 1583 - 1719

136 7099 26374 1970 - 2106

136 7100 454378 1617 - 1753

136 7101 8136 1598 - 1734

137 7146 1907246 1585 - 1722

137 7147 1204683 1583 - 1720

137 7150 935288 1584 - 1721

137 7151 1652783 1587 - 1724

138 7196 36395 1680 - 1818

138 7197 920432 1585 - 1723

138 7198 55919 1609 - 1747

138 7200 1560 5753 - 5891

138 7201 3531174 1583 - 1721

138 7202 1154520 1586 - 1724

139 7251 625318 1612 - 1751

139 7252 3979237 1583 - 1722

139 7253 9008 2133 - 2272

139 7255 14896 1994 - 2133

139 7256 952833 1587 - 1726

139 7257 118708 1595 - 1734

140 7302 1320743 1585 - 1725

140 7303 1193637 1583 - 1723

140 7306 876737 1605 - 1745

140 7307 2308883 1584 - 1724

141 7353 347518 1590 - 1731

141 7354 67679 1609 - 1750

141 7357 3534944 1584 - 1725

141 7358 1749859 1583 - 1724

142 7407 297429 1629 - 1771

142 7408 3616194 1583 - 1725

142 7409 102391 1602 - 1744

142 7411 2880 5749 - 5891

142 7412 1350632 1584 - 1726

142 7413 330474 1592 - 1734

143 7458 834926 1585 - 1728

143 7459 1081905 1590 - 1733

143 7462 717500 1605 - 1748

143 7463 3065669 1583 - 1726

144 7509 3672 2190 - 2334

144 7510 2664 2171 - 2315

144 7513 3148249 1584 - 1728

144 7514 2356727 1583 - 1727

144 7517 85487 1723 - 1867

144 7518 103201 1704 - 1848

145 7563 92224 1680 - 1825

145 7564 3108423 1583 - 1728

145 7565 217818 1599 - 1744

145 7568 1629519 1584 - 1729

145 7569 652016 1589 - 1734

146 7614 449919 1585 - 1731

146 7615 869363 1590 - 1736

146 7618 502627 1605 - 1751

146 7619 3832917 1583 - 1729

146 7620 45174 1598 - 1744

147 7669 2380933 1584 - 1731

147 7670 2539166 1583 - 1730

147 7673 211421 1625 - 1772

147 7674 568480 1587 - 1734

148 7720 2475657 1583 - 1731

148 7721 345259 1596 - 1744

148 7724 1801679 1584 - 1732

148 7725 1077405 1586 - 1734

149 7770 166531 1612 - 1761

149 7771 554578 1590 - 1739

149 7772 624 5891 - 6040

149 7774 246770 1656 - 1805

149 7775 4581138 1583 - 1732

149 7776 150359 1595 - 1744

150 7825 1728633 1585 - 1735

150 7826 2593917 1583 - 1733

150 7829 221609 1625 - 1775

150 7830 1152899 1584 - 1734

150 7831 2942 4047 - 4197

151 7876 1758942 1585 - 1736

151 7877 464425 1593 - 1744

151 7880 1873340 1584 - 1735

151 7881 1603293 1583 - 1734

152 7926 6045 1666 - 1818

152 7927 125435 1590 - 1742

152 7930 4432 2573 - 2725

152 7931 5164643 1583 - 1735

152 7932 392149 1592 - 1744

152 7935 6232 2315 - 2467

152 7936 1064 6703 - 6855

153 7981 1174681 1585 - 1738

153 7982 2550320 1583 - 1736

153 7985 155243 1649 - 1802

153 7986 1792078 1584 - 1737

153 7987 27678 2119 - 2272

154 8032 1137634 1585 - 1739

154 8033 488184 1590 - 1744

154 8036 1849594 1584 - 1738

154 8037 2224588 1583 - 1737

155 8086 12672 2316 - 2471

155 8087 4336417 1583 - 1738

155 8088 877546 1589 - 1744

155 8091 310449 1617 - 1772

155 8092 162916 1598 - 1753

156 8137 715660 1585 - 1741

156 8138 2411792 1583 - 1739

156 8141 64184 1649 - 1805

156 8142 2385712 1584 - 1740

156 8143 122652 1598 - 1754

157 8188 614162 1585 - 1742

157 8189 414107 1590 - 1747

157 8192 1728012 1584 - 1741

157 8193 2943719 1583 - 1740

158 8243 3469188 1583 - 1741

158 8244 1159898 1586 - 1744

158 8247 557968 1587 - 1745

158 8248 512946 1595 - 1753

159 8293 364178 1612 - 1771

159 8294 2158739 1583 - 1742

159 8295 6986 2133 - 2292

159 8297 32264 1744 - 1903

159 8298 2760515 1584 - 1743

159 8299 377318 1595 - 1754

160 8344 196313 1601 - 1761

160 8345 234407 1590 - 1750

160 8348 1500807 1585 - 1745

160 8349 3768473 1583 - 1743

161 8399 2678627 1585 - 1746

161 8400 1352910 1583 - 1744

161 8403 703475 1584 - 1745

161 8404 964988 1592 - 1753

162 8449 149478 1656 - 1818

162 8450 1733079 1585 - 1747

162 8451 49797 1903 - 2065

162 8453 3680 5729 - 5891

162 8454 3027689 1583 - 1745

162 8455 736277 1592 - 1754

163 8500 1584 2190 - 2353

163 8501 7488 2152 - 2315

163 8504 1037517 1585 - 1748

163 8505 4477510 1583 - 1746

163 8508 14257 1970 - 2133

163 8509 160352 1704 - 1867

163 8510 1292 9125 - 9288

164 8555 1988701 1585 - 1749

164 8556 1445287 1583 - 1747

164 8559 748347 1584 - 1748

164 8560 1517665 1589 - 1753

165 8605 34624 1680 - 1845

165 8606 1208542 1585 - 1750

165 8607 91639 1609 - 1774

165 8610 3144240 1583 - 1748

165 8611 1220955 1589 - 1754

166 8660 549830 1585 - 1751

166 8661 4328353 1583 - 1749

166 8662 57439 1903 - 2069

166 8664 6368 5725 - 5891

166 8665 666263 1587 - 1753

166 8666 91747 1598 - 1764

167 8711 1399658 1585 - 1752

167 8712 1436781 1583 - 1750

167 8715 692336 1584 - 1751

167 8716 2171225 1586 - 1753

168 8762 624271 1590 - 1758

168 8763 112985 1609 - 1777

168 8766 3152705 1583 - 1751

168 8767 1810039 1586 - 1754

169 8816 204696 1649 - 1818

169 8817 3997083 1583 - 1752

169 8818 136294 1609 - 1778

169 8821 1055483 1584 - 1753

169 8822 306444 1595 - 1764

170 8867 911262 1585 - 1755

170 8868 1327628 1590 - 1760

170 8871 540443 1605 - 1775

170 8872 2915902 1583 - 1753

170 8873 4765 4047 - 4217

171 8918 95646 1590 - 1761

171 8919 48469 1609 - 1780

171 8922 3034148 1584 - 1755

171 8923 2517329 1583 - 1754

171 8926 2128 2315 - 2486

171 8927 2280 3507 - 3678

172 8972 12896 3229 - 3401

172 8973 3457184 1583 - 1755

172 8974 270444 1602 - 1774

172 8977 1333928 1584 - 1756

172 8978 625548 1592 - 1764

173 9023 518228 1585 - 1758

173 9024 1123113 1590 - 1763

173 9027 335060 1629 - 1802

173 9028 3672197 1583 - 1756

173 9029 51402 1923 - 2096

174 9078 2361017 1584 - 1758

174 9079 2881141 1583 - 1757

174 9082 125851 1655 - 1829

174 9083 331991 1598 - 1772

175 9128 10592 2316 - 2491

175 9129 2633241 1583 - 1758

175 9130 499142 1599 - 1774

175 9133 1517425 1584 - 1759

175 9134 1039600 1589 - 1764

176 9179 223022 1585 - 1761

176 9180 820770 1590 - 1766

176 9183 127906 1629 - 1805

176 9184 4334206 1583 - 1759

176 9185 194096 1598 - 1774

177 9234 1696413 1584 - 1761

177 9235 2948196 1583 - 1760

177 9238 151754 1625 - 1802

177 9239 897284 1587 - 1764

177 9240 6353 4047 - 4224

178 9285 1926859 1583 - 1761

178 9286 618567 1596 - 1774

178 9289 1599937 1584 - 1762

178 9290 1554637 1586 - 1764

179 9335 37718 1639 - 1818

179 9336 403377 1590 - 1769

179 9337 5148 2133 - 2312

179 9339 54232 1724 - 1903

179 9340 4624501 1583 - 1762

179 9341 575024 1595 - 1774

180 9390 1134110 1585 - 1765

180 9391 2912950 1583 - 1763

180 9394 98754 1625 - 1805

180 9395 1518082 1584 - 1764

180 9396 36104 1598 - 1778

181 9441 1300059 1585 - 1766

181 9442 647818 1593 - 1774

181 9445 1581683 1584 - 1765

181 9446 2170440 1583 - 1764

182 9492 9288 2152 - 2334

182 9493 2520 2133 - 2315

182 9496 4444033 1583 - 1765

182 9497 1081045 1592 - 1774

182 9500 113403 1723 - 1905

182 9501 49711 1704 - 1886

183 9546 675529 1585 - 1768

183 9547 2770762 1583 - 1766

183 9548 3220 2133 - 2316

183 9550 47165 1720 - 1903

183 9551 2035556 1584 - 1767

183 9552 167768 1595 - 1778

184 9597 774067 1585 - 1769

184 9598 576261 1590 - 1774

184 9601 1462621 1584 - 1768

184 9602 2887051 1583 - 1767

185 9652 3542672 1583 - 1768

185 9653 1408473 1589 - 1774

185 9656 378998 1587 - 1772

185 9657 369857 1598 - 1783

186 9702 340781 1585 - 1771

186 9703 2481982 1583 - 1769

186 9704 29199 1903 - 2089

186 9706 8024 5181 - 5367

186 9707 2427060 1584 - 1770

186 9708 412954 1592 - 1778

187 9753 348735 1601 - 1788

187 9754 404044 1590 - 1777

187 9757 1242899 1584 - 1771

187 9758 3704322 1583 - 1770

188 9808 2749379 1583 - 1771

188 9809 1604217 1586 - 1774

188 9812 527237 1584 - 1772

188 9813 819167 1595 - 1783

189 9858 116272 1629 - 1818

189 9859 2073366 1585 - 1774

189 9860 64775 1609 - 1798

189 9863 2655688 1583 - 1772

189 9864 789899 1589 - 1778

190 9909 43857 1628 - 1818

190 9910 112893 1590 - 1780

190 9913 902571 1585 - 1775

190 9914 4639159 1583 - 1773

190 9917 152 16709 - 16899

190 9918 1368 3507 - 3697

191 9964 2054118 1585 - 1776

191 9965 1701929 1583 - 1774

191 9968 577444 1584 - 1775

191 9969 1366509 1587 - 1778

192 10014 9616 3209 - 3401

192 10015 1524111 1585 - 1777

192 10016 123137 1609 - 1801

192 10019 2773201 1583 - 1775

192 10020 1269935 1586 - 1778

193 10069 424201 1612 - 1805

193 10070 4757537 1583 - 1776

193 10071 75943 1903 - 2096

193 10073 2016 5698 - 5891

193 10074 391555 1617 - 1810

193 10075 48748 1598 - 1791

194 10120 1453841 1585 - 1779

194 10121 1704657 1583 - 1777

194 10124 532667 1608 - 1802

194 10125 2008835 1584 - 1778

195 10170 2800 4292 - 4487

195 10171 873009 1585 - 1780

195 10172 183506 1609 - 1804

195 10175 2792881 1584 - 1779

195 10176 1847804 1583 - 1778

196 10225 115584 1629 - 1825

196 10226 4340387 1583 - 1779

196 10227 204161 1602 - 1798

196 10230 784917 1587 - 1783

196 10231 254951 1595 - 1791

197 10276 954532 1585 - 1782

197 10277 1606417 1583 - 1780

197 10280 408378 1605 - 1802

197 10281 2709217 1584 - 1781

197 10282 21456 2119 - 2316

198 10327 318554 1590 - 1788

198 10328 143212 1609 - 1807

198 10331 2707882 1584 - 1782

198 10332 2530352 1583 - 1781

199 10381 37656 1724 - 1923

199 10382 3564420 1583 - 1782

199 10383 460507 1599 - 1798

199 10386 1071686 1584 - 1783

199 10387 565731 1592 - 1791

200 10432 555988 1585 - 1785

200 10433 1407412 1590 - 1790

200 10436 217380 1605 - 1805

200 10437 3442252 1583 - 1783

200 10438 76968 1598 - 1798

201 10483 5696 2152 - 2353

201 10484 8803 2114 - 2315

201 10487 2327867 1584 - 1785

201 10488 3207352 1583 - 1784

201 10491 47819 1723 - 1924

201 10492 102463 1704 - 1905

202 10538 2808916 1583 - 1785

202 10539 656118 1596 - 1798

202 10542 1257448 1584 - 1786

202 10543 977518 1589 - 1791

203 10588 260827 1585 - 1788

203 10589 1102744 1590 - 1793

203 10590 2280 2133 - 2336

203 10592 88562 1700 - 1903

203 10593 3949824 1583 - 1786

203 10594 295763 1595 - 1798

204 10643 1645680 1584 - 1788

204 10644 3320988 1583 - 1787

204 10647 91908 1625 - 1829

204 10648 640164 1587 - 1791

204 10649 1260 8685 - 8889

205 10694 2079204 1583 - 1788

205 10695 788281 1593 - 1798

205 10698 1342106 1584 - 1789

205 10699 1490409 1586 - 1791

206 10744 74584 1612 - 1818

206 10745 681147 1590 - 1796

206 10746 12571 2106 - 2312

206 10748 9832 5161 - 5367

206 10749 4256313 1583 - 1789

206 10750 665553 1592 - 1798

***************************************************

2849994 148705560 1206307 1585 - 2851579

2849994 148705561 2838743 1583 - 2851577

2849994 148705562 48 31103 - 2881097

2849994 148705564 111727 1625 - 2851619

2849994 148705565 1515297 1584 - 2851578

2849994 148705566 27878 1598 - 2851592

2849995 148705611 1337669 1585 - 2851580

2849995 148705612 608246 1593 - 2851588

2849995 148705615 1637421 1584 - 2851579

2849995 148705616 2116664 1583 - 2851578

2849996 148705662 96 45201 - 2895197

2849996 148705663 32 22403 - 2872399

2849996 148705666 4550997 1583 - 2851579

2849996 148705667 995479 1592 - 2851588

2849996 148705670 108979 1723 - 2851719

2849996 148705671 44417 1704 - 2851700

2849997 148705716 738321 1585 - 2851582

2849997 148705717 2708004 1583 - 2851580

2849997 148705718 1224 5739 - 2855736

2849997 148705720 22514 1798 - 2851795

2849997 148705721 2115380 1584 - 2851581

2849997 148705722 114557 1595 - 2851592

2849998 148705767 803912 1585 - 2851583

2849998 148705768 544454 1590 - 2851588

2849998 148705771 1526124 1584 - 2851582

2849998 148705772 2825510 1583 - 2851581

2849999 148705822 3632112 1583 - 2851582

2849999 148705823 1317071 1589 - 2851588

2849999 148705826 382906 1587 - 2851586

2849999 148705827 367911 1598 - 2851597

2850000 148705872 368800 1585 - 2851585

2850000 148705873 2481200 1583 - 2851583

2850000 148705877 2481200 1584 - 2851584

2850000 148705878 368800 1592 - 2851592

There is a break after the 206 years-apart calculation followed by y years-apart results for 2849994 <= y <= 2850000. I have included these in order to better illustrate what happens next. Take a look at the last two weeks-apart entries: Their frequencies mirror the frequencies of the previous two entries. This is no coincidence: It seems that for every weeks-apart w < 148705875, there exists a weeks-apart 297411750-w whose frequency is identical to that of w. That symmetry will bring us all the way to 297411750, the only possible weeks-apart for Easters exactly 5700000 years-apart. And every weeks-apart greater than 297411750 is simply the sum of a weeks-apart less than 297411750 plus some positive multiple of 297411750. Thus the enumeration above, ending with weeks-apart 148705873, encapsulates the history of the entire sequence to infinity.

Of course, it's only a partial enumeration: years-apart from 207 to 2849993 are missing, so one may legitimately wonder what surprises (if any) might be in store. Are there any frequency examples smaller than 32? Can there exist 8 solutions for a given years-apart? Can all the weeks-apart solutions for a given years-apart ever be consecutive? And finally, a question that can only be answered by calculating the entire list: What is the index in A134691 of the term 148705873?