Some New Word-Discoveries in Base-26 Pi

Some New Word-Discoveries in Base-26 Pi

I was alerted to Mike Keith's The Pi Code through Ivars Peterson's Math Trek (April Fool's) spoof of it. Pi is expressed numerically in base 26, and then the 26 different base-26 digits are identified with letters as 0=a, 1=b, 2=c,... 25=z.

I was interested in finding, in the expression, occurrences of the strings "three", "eight", "eleven", and greater. Also, I hoped to find an example of an 8-letter English word.

My Mathematica 4 code is pretty straighforward:

p = FromCharacterCode[97 + First[RealDigits[Pi, 26, 5000010]]];

Calculating these 5 million terms took about 127 hours on a 300 MHz G3. [2.5 million terms requires about 32 hours; 1 million terms, a mere 5 hours.]

numbers = {"zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen", "twenty", "twentyone", "twentytwo", "twentythree", "twentyfour", "twentyfive", "twentysix", "twentyseven", "twentyeight", "twentynine", "thirty", "thirtyone", "thirtytwo", "thirtythree", "thirtyfour", "thirtyfive", "thirtysix", "thirtyseven", "thirtyeight", "thirtynine", "forty", "fortyone", "fortytwo", "fortythree", "fortyfour", "fortyfive", "fortysix", "fortyseven", "fortyeight", "fortynine", "fifty", "fiftyone", "fiftytwo", "fiftythree", "fiftyfour", "fiftyfive", "fiftysix", "fiftyseven", "fiftyeight", "fiftynine", "sixty", "sixtyone", "sixtytwo", "sixtythree", "sixtyfour", "sixtyfive", "sixtysix", "sixtyseven", "sixtyeight", "sixtynine", "seventy", "seventyone", "seventytwo", "seventythree", "seventyfour", "seventyfive", "seventysix", "seventyseven", "seventyeight", "seventynine", "eighty", "eightyone", "eightytwo", "eightythree", "eightyfour", "eightyfive", "eightysix", "eightyseven", "eightyeight", "eightynine", "ninety", "ninetyone", "ninetytwo", "ninetythree", "ninetyfour", "ninetyfive", "ninetysix", "ninetyseven", "ninetyeight", "ninetynine", "hundred", "thousand", "million", "billion", "trillion", "googol"};

t = Table[If[StringPosition[p, numbers[[i]]] == {}, {0}, First[Transpose[StringPosition[p, numbers[[i]]]]] - 1], {i, 1, Length[numbers]}]

And the result:

{{389247, 477606, 878648, 1104661, 1433305, 1676721, 1817430, 3619823, 4399281}, {10087, 16228, 67680, 90346, 93116, 100745, 113692, 131468, 133271, 147576, 165317, 192662, 200004, 203821, 223293, 270767, 279646, 284163, 289718, 312414, 355802, 372750, 379472, 462527, 478648, 519037, 561810, 567560, 599115, 609980, 633202, 670924, 676030, 682689, 687688, 711603, 712631, 720256, 729328, 730945, 771489, 775244, 777753, 784837, 836798, 868082, 906858, 917175, 922929, 1022727, 1035226, 1059296, 1089095, 1111268, 1137119, 1169416, 1174495, 1178425, 1189353, 1197278, 1215245, 1219666, 1243297, 1272504, 1288160, 1294211, 1309427, 1322721, 1341505, 1378997, 1384711, 1425081, 1425911, 1435240, 1470339, 1485262, 1507012, 1579068, 1592059, 1604395, 1614748, 1615213, 1641914, 1643684, 1648385, 1662016, 1677739, 1691026, 1725276, 1736991, 1748159, 1776931, 1803700, 1845120, 1849504, 1851559, 1883548, 1907371, 1919393, 1922579, 1930215, 1933363, 1945967, 1950300, 1951932, 1983773, 1984039, 1987100, 2007597, 2056778, 2060815, 2089212, 2127742, 2146407, 2156670, 2158897, 2173248, 2192530, 2226346, 2228230, 2237405, 2276324, 2278100, 2302280, 2308722, 2311230, 2385959, 2407956, 2412063, 2418410, 2434723, 2435698, 2472944, 2508831, 2521894, 2536235, 2541267, 2577810, 2598253, 2621688, 2624141, 2649103, 2651257, 2688649, 2688953, 2695388, 2697350, 2710972, 2726801, 2763517, 2765782, 2766706, 2795223, 2803654, 2808954, 2857591, 2881250, 2894655, 2897199, 2973600, 2978093, 2978937, 3052620, 3078823, 3094126, 3106543, 3132233, 3148965, 3191072, 3233577, 3237182, 3254885, 3303519, 3360353, 3367699, 3370339, 3374466, 3384481, 3397312, 3405843, 3458494, 3485926, 3486911, 3489640, 3504654, 3508820, 3515214, 3522140, 3524426, 3550982, 3552700, 3553295, 3571494, 3605477, 3620480, 3665262, 3675077, 3679999, 3683818, 3695165, 3699815, 3700074, 3703222, 3721525, 3730685, 3748637, 3757307, 3779468, 3804305, 3806985, 3820738, 3821751, 3825602, 3860955, 3888573, 3904169, 3928017, 3940157, 3944130, 3998713, 4000630, 4007432, 4025047, 4041308, 4043025, 4046055, 4052622, 4064231, 4104699, 4123361, 4124155, 4134103, 4145340, 4169188, 4195970, 4218503, 4233924, 4262406, 4268756, 4326878, 4337338, 4377585, 4388911, 4427462, 4450735, 4471892, 4475424, 4475653, 4478810, 4493300, 4500178, 4526432, 4545997, 4554866, 4559684, 4572456, 4585191, 4610438, 4623673, 4636158, 4647372, 4658462, 4676669, 4677033, 4689112, 4706331, 4708379, 4741869, 4754090, 4764491, 4775709, 4784374, 4805207, 4807906, 4901880, 4932215, 4969093, 4974188, 4985658}, {13463, 18048, 26710, 62389, 63239, 67531, 75003, 80287, 96106, 97541, 102199, 164910, 178919, 183389, 187650, 194028, 204554, 211394, 224397, 243816, 283243, 287956, 288242, 301016, 321320, 332911, 347072, 351134, 383491, 387202, 459260, 468272, 472045, 485230, 485902, 516333, 516918, 544134, 547166, 548517, 573271, 583215, 612930, 643834, 655268, 662036, 667110, 686632, 691729, 772879, 780254, 786958, 789324, 800863, 805474, 824462, 825276, 827515, 851416, 862131, 864087, 869592, 869673, 888111, 889168, 891975, 941271, 946137, 973145, 1097619, 1098324, 1113109, 1119660, 1126840, 1183471, 1202786, 1294525, 1380104, 1402797, 1412999, 1467134, 1472807, 1488582, 1501711, 1537881, 1543846, 1600679, 1605126, 1611704, 1612951, 1613847, 1620725, 1628802, 1632846, 1634879, 1639647, 1646050, 1665501, 1719767, 1733411, 1752908, 1764138, 1767416, 1774864, 1790058, 1811049, 1820618, 1831261, 1832934, 1835271, 1852053, 1857163, 1863491, 1880658, 1941211, 1945319, 1950395, 1955931, 2002942, 2023548, 2044883, 2065305, 2109365, 2150353, 2195242, 2198284, 2206025, 2206227, 2213430, 2217638, 2241660, 2285102, 2288409, 2290053, 2335136, 2395958, 2405222, 2470578, 2480488, 2484500, 2501622, 2508388, 2522484, 2523739, 2576007, 2604986, 2605671, 2652736, 2671831, 2685799, 2704344, 2706736, 2708764, 2740093, 2778567, 2797750, 2798092, 2806527, 2832311, 2840634, 2845424, 2849605, 2865573, 2883119, 2883949, 2885172, 2890434, 2892360, 2924655, 2924705, 2942866, 2962917, 2966896, 2973159, 3017560, 3028461, 3035502, 3042278, 3054226, 3061896, 3064712, 3073718, 3094796, 3096266, 3099061, 3104950, 3137054, 3145531, 3184445, 3190863, 3202261, 3207811, 3208801, 3220736, 3231222, 3234998, 3239997, 3285786, 3310637, 3320837, 3328427, 3349197, 3368760, 3450680, 3451028, 3452033, 3461331, 3473401, 3523093, 3530339, 3579501, 3593313, 3639595, 3640893, 3713696, 3752728, 3758432, 3765368, 3796492, 3830883, 3845340, 3853260, 3857243, 3872346, 3920993, 3921000, 3928561, 3933326, 3941141, 3944985, 3974146, 4040139, 4059782, 4083352, 4102087, 4114515, 4118898, 4119408, 4129792, 4150943, 4177893, 4179551, 4184517, 4204088, 4209598, 4210302, 4210494, 4224044, 4236422, 4237060, 4241813, 4262079, 4273350, 4279473, 4281078, 4298538, 4313849, 4319593, 4324974, 4330788, 4330803, 4336979, 4348106, 4352012, 4375998, 4400315, 4426196, 4460191, 4468730, 4476579, 4502682, 4527631, 4532982, 4549317, 4560855, 4577949, 4584837, 4588817, 4590775, 4599022, 4604973, 4622574, 4629369, 4645605, 4648443, 4733963, 4737574, 4749823, 4759392, 4793417, 4794837, 4804490, 4830050, 4866206, 4901169, 4911651, 4912517, 4913219, 4920533, 4926894, 4931421, 4979016, 4988648}, {1556763}, {11324, 1357212, 2102467, 2598342, 3598568, 4531170, 4753873}, {64838, 532611, 818548, 1524576, 2185271, 2292443, 2500443, 3251581, 3285603, 3975083, 4220318, 4379682}, {14295, 34094, 41647, 120213, 125240, 130061, 137515, 140085, 197748, 243959, 261278, 268634, 270646, 281091, 288509, 290676, 302021, 324065, 325681, 330057, 358642, 377088, 420511, 427124, 438172, 448482, 459642, 486028, 488585, 537704, 546637, 557713, 583901, 584440, 589438, 617284, 649073, 650571, 667509, 695684, 699142, 713510, 733959, 739780, 746377, 815456, 837890, 839628, 857096, 905691, 921685, 926408, 930927, 938346, 959684, 975141, 984030, 988584, 1041648, 1047218, 1055885, 1056416, 1071665, 1074404, 1094469, 1137275, 1144940, 1145642, 1176250, 1178147, 1223558, 1228510, 1229276, 1230272, 1274434, 1289088, 1317094, 1328111, 1337122, 1338665, 1358115, 1386243, 1393694, 1400622, 1444306, 1446411, 1460697, 1522373, 1523741, 1527367, 1530120, 1533049, 1543533, 1560108, 1572253, 1575767, 1588707, 1588761, 1603844, 1635008, 1654431, 1672065, 1682532, 1698938, 1707889, 1712791, 1734162, 1734388, 1742063, 1759818, 1760927, 1761935, 1771593, 1809581, 1827017, 1875515, 1897073, 1933285, 1939434, 1941910, 1984844, 2001203, 2047592, 2123719, 2125881, 2131007, 2135074, 2152028, 2157299, 2182159, 2184966, 2206421, 2230167, 2241720, 2263685, 2287434, 2308561, 2308610, 2311308, 2313717, 2317035, 2319077, 2344948, 2348777, 2396958, 2397025, 2400902, 2410349, 2428559, 2438026, 2486032, 2515748, 2528718, 2549348, 2555226, 2562312, 2562617, 2562988, 2565049, 2567475, 2571153, 2603320, 2608225, 2611742, 2657104, 2668807, 2796889, 2811366, 2818702, 2819476, 2820933, 2836558, 2855860, 2869203, 2869780, 2874502, 2884584, 2925286, 2927525, 2940645, 2972153, 2978555, 2981642, 2981730, 2995874, 3051950, 3071353, 3072950, 3084927, 3086507, 3091243, 3100563, 3115772, 3130071, 3148546, 3153718, 3155772, 3163298, 3170361, 3182757, 3192953, 3199250, 3202537, 3230439, 3246526, 3259146, 3282331, 3284523, 3319171, 3342058, 3363162, 3371023, 3379128, 3396826, 3400772, 3402886, 3407678, 3430688, 3464650, 3467615, 3475095, 3486294, 3514279, 3522305, 3533613, 3546720, 3627466, 3642832, 3679193, 3703037, 3713458, 3722357, 3728312, 3756421, 3765421, 3802001, 3818817, 3819939, 3839469, 3840167, 3875725, 3879960, 3888486, 3905760, 3917570, 3932330, 3938440, 3940785, 3972595, 3975983, 3977711, 4043269, 4045620, 4088526, 4120623, 4156548, 4190293, 4261414, 4262656, 4269175, 4279011, 4309522, 4337534, 4349393, 4388617, 4420297, 4448535, 4473243, 4474756, 4486270, 4495391, 4510217, 4516113, 4521965, 4526947, 4536832, 4554197, 4562614, 4565993, 4573197, 4622545, 4636266, 4647584, 4668688, 4671283, 4700033, 4713286, 4758961, 4770708, 4813085, 4820061, 4828519, 4831919, 4862667, 4867375, 4897678, 4901876, 4924208, 4936906, 4957160, 4994867}, {786244}, {0}, {175372, 345722, 1753703, 3195595, 3834692, 4483124, 4924923}, {15276, 34990, 50052, 86941, 129910, 140864, 162582, 165914, 182947, 228703, 253510, 255109, 294379, 329126, 376856, 395776, 396153, 408328, 431882, 432679, 439345, 450363, 470406, 499796, 502178, 506674, 533019, 549315, 566237, 571411, 591060, 601579, 608771, 660060, 665786, 674350, 682703, 696255, 707788, 731182, 747348, 759579, 765360, 786111, 797921, 811779, 817343, 827903, 839236, 850251, 963782, 984184, 984877, 1018339, 1024434, 1029264, 1057115, 1074425, 1096066, 1102671, 1114118, 1207070, 1240473, 1245269, 1270643, 1297285, 1299019, 1303219, 1323637, 1325097, 1368854, 1374574, 1444420, 1453562, 1468415, 1471960, 1485072, 1498895, 1532388, 1563848, 1592429, 1592460, 1594897, 1598908, 1620373, 1673108, 1681492, 1696622, 1699741, 1701567, 1706375, 1737940, 1768687, 1771927, 1777932, 1782401, 1797267, 1806786, 1806997, 1809630, 1813195, 1818408, 1826285, 1833243, 1843447, 1881621, 1930652, 1953651, 1989620, 2019597, 2092078, 2098979, 2115838, 2152006, 2182973, 2196859, 2234509, 2237772, 2245996, 2263814, 2266608, 2276061, 2279152, 2289474, 2295458, 2297519, 2316224, 2366305, 2378211, 2423835, 2427410, 2432279, 2433907, 2448759, 2474233, 2482125, 2495738, 2579929, 2595540, 2599768, 2608377, 2634263, 2642248, 2650161, 2681849, 2683604, 2724369, 2754214, 2755843, 2783404, 2788569, 2804316, 2818057, 2822340, 2840819, 2840978, 2893340, 2915448, 2930944, 2964179, 2989046, 2999563, 3046837, 3047317, 3054315, 3072329, 3082769, 3109929, 3122706, 3128501, 3134538, 3141490, 3142785, 3152863, 3156015, 3183792, 3185737, 3194631, 3231091, 3261509, 3274302, 3287968, 3328695, 3330431, 3362598, 3383868, 3467054, 3475129, 3515605, 3535138, 3555075, 3585995, 3603103, 3618299, 3667721, 3684494, 3693380, 3699983, 3701536, 3739717, 3754412, 3759297, 3772448, 3787926, 3794846, 3798277, 3835658, 3839236, 3873135, 3886671, 3888115, 3890453, 3930486, 3933640, 3990811, 4017775, 4082602, 4125166, 4128492, 4210922, 4222392, 4226655, 4230938, 4231528, 4242903, 4256880, 4264435, 4268061, 4277136, 4332886, 4337774, 4349338, 4368741, 4373388, 4380157, 4382342, 4382827, 4393698, 4411026, 4419406, 4421097, 4430877, 4443566, 4459210, 4468783, 4499013, 4525054, 4526353, 4570523, 4575693, 4589065, 4591309, 4594048, 4723617, 4724421, 4727181, 4753584, 4772325, 4778628, 4802737, 4810150, 4818568, 4834742, 4861387, 4864380, 4872592, 4880654, 4931941, 4939846, 4945462, 4954066, 4969314, 4969452}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {2300987, 4896456}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}}

So we got a hit for "three" and two for "fifty" (I've indicated these, as well as the already-known "seven", above and below), but other number names are still unknown. Mike Keith organizes these sets into the order in which the number-words occur:

1426122662252122112212166611661219222126112212266661162122616261266629221616...

...having, obviously, deleted occasions of "ten" from the sequence. The following list will be that sequence within the new larger (5-million-term) range, but I won't exclude "ten", and the newly discovered "fifty", from the set:

{1, 4, 2, 6, 10, 1, 2, 2, 6, 10, 6, 10, 2, 2, 5, 2, 1, 2, 2, 10, 1, 1, 2, 2, 1, 2, 1, 6, 6, 10, 6, 1, 1, 6, 6, 10, 1, 10, 2, 1, 10, 9, 2, 10, 2, 2, 1, 2, 6, 1, 1, 2, 2, 1, 2, 10, 2, 6, 10, 10, 6, 6, 6, 1, 1, 6, 2, 1, 2, 2, 6, 1, 6, 10, 2, 6, 1, 2, 6, 6, 10, 6, 2, 9, 2, 2, 1, 6, 1, 10, 6, 1, 2, 2, 0, 10, 10, 10, 6, 6, 10, 10, 6, 10, 6, 10, 2, 6, 1, 2, 10, 2, 0, 1, 2, 2, 6, 6, 10, 10, 10, 2, 2, 1, 5, 10, 6, 2, 6, 2, 2, 10, 6, 1, 10, 1, 10, 2, 2, 6, 6, 6, 10, 1, 10, 10, 1, 2, 6, 1, 2, 6, 6, 2, 10, 2, 10, 2, 6, 1, 10, 1, 1, 10, 2, 1, 2, 6, 10, 6, 10, 1, 1, 6, 1, 1, 1, 10, 6, 6, 6, 10, 10, 10, 1, 2, 1, 1, 2, 1, 10, 7, 2, 2, 10, 2, 2, 10, 6, 10, 5, 2, 2, 2, 10, 1, 6, 10, 6, 10, 2, 6, 2, 2, 1, 2, 2, 0, 2, 2, 2, 6, 1, 1, 6, 1, 6, 6, 6, 2, 2, 6, 10, 2, 6, 6, 10, 10, 6, 10, 1, 10, 10, 1, 6, 6, 6, 6, 10, 1, 6, 6, 10, 1, 6, 10, 2, 2, 10, 0, 1, 2, 10, 2, 2, 1, 6, 6, 6, 1, 1, 6, 6, 1, 2, 1, 1, 2, 10, 1, 1, 6, 6, 6, 6, 10, 1, 10, 10, 1, 6, 1, 6, 1, 2, 10, 10, 10, 1, 6, 1, 10, 10, 6, 6, 6, 1, 4, 6, 10, 10, 1, 2, 1, 6, 6, 6, 2, 2, 1, 1, 0, 1, 6, 10, 6, 10, 6, 2, 10, 1, 10, 2, 10, 1, 2, 10, 2, 1, 6, 6, 5, 6, 6, 10, 6, 2, 6, 2, 3, 6, 10, 6, 6, 1, 6, 6, 1, 10, 10, 10, 10, 2, 6, 1, 2, 2, 2, 2, 1, 1, 10, 2, 2, 2, 2, 6, 2, 1, 1, 2, 1, 6, 1, 2, 6, 10, 0, 1, 10, 6, 1, 10, 6, 10, 10, 10, 6, 6, 2, 1, 2, 6, 6, 1, 10, 6, 1, 2, 9, 6, 6, 6, 2, 2, 10, 6, 10, 2, 1, 10, 10, 2, 10, 1, 10, 10, 6, 10, 2, 10, 0, 10, 2, 10, 6, 2, 2, 10, 2, 10, 1, 1, 1, 2, 2, 2, 6, 2, 10, 1, 6, 1, 1, 1, 1, 10, 6, 1, 6, 2, 6, 2, 1, 1, 2, 1, 10, 2, 1, 1, 6, 1, 10, 6, 2, 1, 10, 2, 2, 6, 1, 1, 2, 1, 10, 10, 4, 2, 10, 6, 6, 1, 6, 6, 1, 2, 10, 6, 1, 6, 1, 1, 6, 10, 6, 5, 1, 2, 10, 2, 2, 2, 6, 2, 2, 1, 1, 6, 10, 1, 10, 2, 6, 10, 6, 10, 10, 10, 1, 1, 10, 2, 6, 2, 10, 2, 5, 10, 10, 50, 1, 6, 6, 1, 1, 6, 6, 10, 6, 6, 2, 6, 6, 10, 10, 1, 2, 6, 6, 6, 2, 1, 6, 1, 1, 10, 10, 6, 10, 10, 1, 1, 6, 10, 2, 1, 10, 2, 10, 2, 6, 10, 5, 2, 2, 1, 6, 1, 2, 2, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 2, 1, 10, 10, 1, 4, 10, 6, 2, 2, 6, 10, 6, 1, 1, 10, 10, 1, 10, 1, 2, 6, 6, 2, 10, 10, 2, 1, 1, 1, 1, 2, 2, 2, 1, 10, 1, 2, 10, 10, 1, 1, 1, 2, 10, 10, 1, 6, 2, 2, 1, 10, 2, 1, 6, 10, 6, 6, 6, 10, 2, 6, 2, 10, 10, 2, 2, 6, 1, 2, 6, 6, 6, 1, 2, 2, 6, 2, 2, 2, 10, 1, 1, 10, 2, 2, 6, 6, 10, 6, 2, 2, 10, 2, 6, 2, 1, 1, 6, 1, 6, 6, 10, 6, 10, 2, 2, 2, 2, 10, 10, 6, 1, 2, 10, 2, 2, 6, 10, 6, 2, 1, 10, 6, 6, 6, 1, 2, 2, 2, 6, 2, 1, 10, 6, 10, 10, 6, 1, 10, 2, 10, 10, 2, 6, 1, 10, 6, 6, 10, 6, 6, 6, 10, 2, 10, 2, 1, 6, 10, 9, 6, 2, 6, 2, 2, 2, 6, 10, 2, 1, 2, 1, 2, 6, 5, 1, 6, 10, 10, 6, 6, 5, 2, 10, 1, 2, 6, 2, 2, 10, 10, 6, 2, 1, 10, 6, 1, 2, 1, 6, 1, 6, 10, 1, 6, 1, 6, 6, 1, 6, 6, 2, 2, 2, 1, 2, 6, 10, 6, 2, 6, 10, 1, 6, 1, 1, 1, 1, 6, 1, 10, 1, 6, 2, 1, 2, 6, 10, 6, 1, 1, 1, 10, 1, 2, 10, 2, 4, 10, 1, 10, 0, 1, 6, 2, 2, 6, 1, 10, 1, 6, 1, 1, 10, 10, 1, 1, 10, 1, 10, 6, 1, 6, 2, 1, 6, 6, 1, 10, 1, 2, 10, 6, 1, 2, 10, 2, 6, 10, 1, 10, 10, 2, 10, 6, 1, 1, 6, 6, 1, 1, 1, 2, 9, 10, 10, 6, 6, 2, 2, 2, 1, 2, 10, 6, 6, 10, 10, 6, 1, 10, 1, 6, 6, 2, 2, 1, 2, 10, 6, 2, 10, 6, 1, 6, 2, 1, 2, 6, 2, 5, 6, 6, 10, 1, 1, 1, 10, 1, 2, 1, 1, 6, 6, 1, 1, 2, 1, 10, 2, 6, 2, 1, 2, 2, 2, 6, 1, 1, 10, 10, 2, 1, 1, 2, 6, 1, 2, 2, 2, 6, 1, 2, 2, 2, 2, 10, 1, 5, 10, 2, 10, 10, 10, 1, 2, 2, 2, 10, 10, 6, 2, 1, 6, 10, 10, 1, 6, 2, 10, 6, 2, 2, 2, 6, 2, 2, 2, 1, 2, 2, 10, 2, 1, 6, 10, 2, 10, 6, 2, 10, 10, 2, 1, 5, 10, 10, 10, 6, 1, 10, 0, 2, 10, 10, 6, 10, 2, 1, 10, 10, 6, 1, 10, 2, 2, 10, 1, 6, 6, 1, 1, 2, 1, 9, 6, 1, 6, 10, 1, 2, 6, 6, 6, 10, 10, 1, 6, 2, 4, 2, 6, 1, 2, 6, 1, 1, 2, 6, 6, 10, 1, 6, 10, 2, 2, 1, 2, 10, 2, 10, 10, 2, 2, 1, 6, 2, 1, 2, 1, 6, 2, 1, 6, 2, 1, 6, 6, 1, 1, 1, 6, 1, 1, 6, 10, 10, 10, 2, 2, 1, 2, 10, 4, 1, 6, 2, 1, 6, 10, 1, 10, 1, 2, 2, 10, 2, 1, 1, 10, 6, 10, 6, 6, 2, 6, 10, 10, 6, 10, 2, 6, 10, 10, 50, 6, 2, 6, 1, 2, 2, 2, 2, 6, 9, 2, 2, 10, 1, 6, 10, 10, 10, 6, 1, 10, 10, 1, 2, 1, 2, 6, ...}

Addendum: I've just come across the words 'myriad' for 10^4, 'lac' (or 'lakh') for 10^5, and 'crore' for 10^7 (in Conway & Guy's wonderful 'Book of Numbers'). I do not believe these words enjoy sufficient (English) currency to merit inclusion in the above. However, for the record, 'myriad' does not yet appear; 'crore' at {2575134}; and 'lac' ('lakh'), as would be expected, make almost 300 appearances, beginning with {11452, 28471, 59389, ...}.

Eight-Letter Words

Sifting through a set of 52884 eight-letter-word possibles culled from a word-list, I managed to get one hit at index 3095146: "armagnac".

Backwords: We find the 8-letter strings {"reredner", "naelorit", "koobdreh"} at indices {1013428, 2411562, 3005779}. These are the reversals of {"renderer", "tirolean", "herdbook"}.

Seven-Letter Words

Sifting through a set of 43208 seven-letter-word possibles...

{{subplot, 115042}, {conjure, 246556}, {talcing, 320929}, {adenlng, 600672}, {dewfall, 883265}, {redbone, 1272500}, {jacamar, 1298666}, {sawlike, 1443539}, {helipad, 1447671}, {painful, 1850810}, {cabbies, 2299545}, {bluetop, 2314274}, {joulean, 2404919}, {impress, 2514918}, {tillich, 2744200}, {rockety, 2785173}, {scowler, 2932496}, {favored, 3064246}, {levants, 3219126}, {socotri, 3222221}, {skeered, 3327305}, {moneran, 3486910}, {urolith, 3545896}, {shittah, 3664605}, {koreans, 3695731}, {pigmies, 3811640}, {taunter, 4152721}, {hotbeds, 4245827}, {helmand, 4550614}, {huddled, 4633306}, {patiala, 4634639}}

Caveat: Of course, word-lists can be problematic. There are likely words that exist that have not found themselves into a given word-list. Conversely, any such list is likely to contain many spurious entries: Who - but the individual who used "adenlng" as an abbreviation for "adenocarcinoma of lung" on some web-based picture-labels - would recognize it as a word?

Having said that, bigger nets catch rarer fish. To wit: Mike Keith missed the word "talcing" in his million base-26-digits search. I wish there was an "Oxford" reference word-list containing every "word" in the OED.

Bottom line: I make no apologies for the found "words". I leave it to logophiles with big dictionaries (and lots of time) to confirm, or deny, entries.

Backwords:

{{naheehs, 66522, sheehan}, {spukcom, 95881, mockups}, {nrohpla, 458065, alphorn}, {tselluf, 468083, fullest}, {rehcsna, 570395, anscher}, {eadilyh, 695334, hylidae}, {desived, 1131041, devised}, {suortic, 1518787, citrous}, {sliaweb, 1675254, bewails}, {sregnil, 2013590, lingers}, {seximnu, 2323053, unmixes}, {daicnud, 2359556, dunciad}, {sehtrig, 2490793, girthes}, {oleujap, 2499558, pajuelo}, {orezbus, 2553716, subzero}, {deillat, 2584224, tallied}, {etanodi, 2656987, idonate}, {mussime, 2860339, emissum}, {esollac, 2883782, callose}, {seizahg, 3448514, ghazies}, {yawaylf, 3494949, flyaway}, {walctac, 3704717, catclaw}, {rednerp, 3813966, prender}, {sretuor, 3844180, routers}, {etilleb, 3920574, bellite}, {sircape, 3928197, epacris}, {ihcugon, 3986308, noguchi}, {siniffa, 4058467, affinis}, {aimeroc, 4123616, coremia}, {gnigniw, 4203061, winging}, {srotteb, 4259672, bettors}, {renobed, 4287056, deboner}, {spracse, 4867240, escarps}, {etatlep, 4985188, peltate}}

Six-Letter Words

And, from a set of 30661 six-letter-word possibles...

{oxygen, salify, medics, yarely, howdon, mithai, pannes, cledgy, virial, ingber, icones, nudnik, revete, exidia, prinky, libyan, thingy, ampler, velsen, wooyen, upstep, rebuts, whydah, buteos, polity, kyushu, teensy, guerre, hurroo, avower, corves, osijek, exarch, fogdom, cuphea, bogota, adhaka, sophic, havana, rissoa, clangs, coopts, chinol, bakutu, erivan, uptube, granny, snudge, deific, alters, desire, thatll, beggar, fozier, uratic, wormer, macana, reflee, dosses, optics, urnism, kasper, ovibos, potgun, amount, drover, octopi, bisley, ancone, muring, sozzle, mclour, defied, warted, whilst, pancho, livery, sevres, dosido, minter, ambury, asaron, orgies, strack, geomys, zenith, aponia, retune, tunful, unfull, semper, empery, mutate, voicer, kubera, alfuro, doolie, baldie, buchem, xenons, busher, camper, bullan, scroff, boland, exceed, lyttae, jaquet, cheery, reckla, bansal, skiers, nyberg, gulper, upbind, jissom, dorser, curema, taluto, prismy, finjan, silvas, joyous, relted, reavow, angild, prolog, zurich, bourne, johore, ranier, booing, takins, upshaw, pewage, soiler, winrow, pattie, skyish, razors, bosken, nadirs, diplex, howley, shists, whammo, hecuba, acamar, balawa, sprose, tawses, rooses, lauren, ligand, molder, palame, xenons, texaco, monica, review, nicety, humber, bodian, shtetl, arrame, calote, gooses, runkly, shaula, upwaft, undrag, capite, huppah, hardim, vermin, yolked, mouses, netcha, forint, mikado, antlia, bowing, skewer, battey, anomie, twaite, myosin, pecite, aeolis, tenues, graphy, cetene, urcuyo, lament, upgaze, foucar, falsie, handed, rotang, nuorva, kainyn, jerids, crojik, hobbes, grafts, beckon, urgers, savins, buchem, glance, byelaw, gabble, strunt, untune, brough, dubbin, kelebe, thieve, carrel, spicey, kharif, cellar, reshut, saurus, nihilo, ureter, unnail, spheno, trashy, etamin, nygmia, dehkan, vadose, dunger, dalles, jimper, blader, lagans, adsorb, anicut, snying, canopy, maniva, agapae, vatter, cabbie, sisson, nimmer, frumpy, secohm, greeni, simous, tedium, giarre, haiduk, wabash, ruffes, neatly, menhir, giaour, polyak, burker, blumba, dische, pinene, uploom, tgamma, slitch, jocose, adsbud, divest, lecerf, ticket, street, divide, multan, atpase, vienna, beento, childr, gimbal, ionone, conger, illich, tenues, machos, mafura, rocket, plower, myelon, fobbed, jiminy, mojave, shored, setlow, ammann, tubbie, meatal, blazon, avaler, kawaka, worldy, doggie, galuth, madcam, werber, thrang, delate, hubshi, oldies, yentai, shouts, josher, skinch, waucht, vipers, edward, revoir, sledge, yodles, hieros, standi, rerigs, levant, unbarb, kawato, jagers, felice, podura, scalar, essays, givers, purify, allure, sponsa, hondas, lakota, saluda, washra, multis, prkacg, scuddy, monera, tasman, leonem, exited, rachel, millie, bigots, sanies, adital, baffed, tamein, epilog, kecked, quartz, korean, domett, imager, elanet, kisser, clysma, honers, pottle, timucu, instal, pownie, tignum, bhavan, bulbil, hardim, softer, skeans, assate, bimbos, geisel, kittel, dessau, cashes, mabolo, capanc, hazers, growse, yantra, hadjes, nuggah, bereft, raping, obstet, dinked, dipsas, welded, barkle, cronin, astony, albula, gossip, spoofy, carnic, tellus, menkes, emmies, staphs, consul, gastri, palade, biting, formee, jersey, screel, meruit, hotbed, kashas, alioth, lupoid, idlety, stroot, parsed, singer, obispo, anopla, abcdef, cyesis, apiary, trisul, vandas, agazed, modulo, hurtle, jumbly, hubert, neurad, larvas, thelma, helman, turion, tracks, nominy, sweven, stoury, binder, analyt, grossa, huddle, bosnia, horses, danton, parker, atolls, ariels, mucose, arusha, gapers, berend, filths, beggar, palais, viable, freity, wharry, meoued, pavins, agalma, bauson, floury, furore, sabins, intube, slypes, denovo, rumbly, ubangi, kelper, lugged, gandhi, atazir, mimers, roggli, vyborg, oxford}

Backwords:

{flouts, fleets, tweaky, blowup, gooses, ebulus, panade, bororo, option, prison, helwig, tolowa, epodes, toilet, harmed, pontil, airest, minyan, phryne, haring, logjam, mockup, flippy, haceks, genevi, relent, unbear, laughy, saboor, ribbed, grumpy, utahan, stuber, spader, rosser, flytes, precut, rooked, faddle, pilots, gasket, daubry, pixley, stelae, nigrum, sradha, curler, premed, roofer, sprack, canaut, whites, comeon, cahows, enacts, gunduz, asquat, cerise, hoover, aditio, bebait, guffer, carack, forpet, timmen, tankah, fixups, betone, pileup, aswing, musang, taniya, giller, phytyl, borgno, haslam, nubere, spence, caucus, edgrew, medway, glumes, gagers, oxwort, serves, zserve, assais, leiden, tashie, swivel, salons, paquet, feline, hexade, whally, mabuse, dehkan, torous, upgang, stance, jaguar, quandy, tapper, queeve, county, leaked, hubcap, libels, folial, canopy, crimea, scrime, martis, pyalla, semola, marver, duplet, stonen, vijver, backup, lusted, taplet, nylast, theirn, pluggy, endere, render, fenton, phakos, radios, bhopal, apodal, hassel, hodful, bahama, devise, zaniah, sartre, phages, salvia, assent, arista, censor, populo, heusen, gonged, yipped, warsel, gorbet, fiance, ethene, copalm, rhodos, lanete, retube, crunch, xavier, portal, chinoa, echino, wotton, double, orthop, kwamme, vittae, ceibas, magahi, savill, mattes, ethnal, lotter, finder, froths, vipery, nerita, sonans, zipper, dewcup, pritch, farads, option, manses, bungle, copita, falsie, inters, bonier, faberg, bewail, titoki, tetany, disant, wildly, lerner, fervet, bonism, muling, alkali, wiling, gulfed, wafted, squibb, cumuli, safety, mooter, clarty, outran, ischia, ceorls, keloid, coughs, wealth, arsino, megrel, caecum, spicae, nontan, outsin, crants, garter, fiddle, scamps, upheld, nudest, shrimp, enjamb, leasow, purges, viddui, molise, snazzy, jabble, frazil, samsun, quotha, linger, tiling, sutton, extort, joliet, rammel, unhelm, desalt, janson, rancor, evejar, midrib, aswell, easels, wuzzle, risser, zarthe, laking, tasian, biafra, baleen, aponia, marion, banian, tarred, glumly, appeal, romish, carobs, geiger, hubble, rerank, chivvy, judice, anglic, knawel, puddee, stuffy, dainty, anotta, garber, atbash, camped, annual, sleepy, femurs, palely, blanco, funori, ugroid, yockel, unawed, frigid, allied, cakile, dhutis, spinal, reared, twiers, mauvis, jactus, selvas, woater, causam, sarkis, donate, orihon, tafias, yogins, sowans, ceiled, hulked, scaley, zamiel, sweepy, lariat, valkyr, gierke, dacrya, devote, illipe, ludlow, bedews, tegmen, balsam, allose, naiant, taxmen, thymus, niloff, griped, beltir, arpens, dienes, watala, ridded, hymner, rebrew, aditio, absens, houdon, byrnie, unfile, euboic, dermis, sayees, borsht, basest, swathe, rinsed, dermal, kedges, tocher, codder, epimer, phonal, ephebi, parley, fogged, beachy, twines, netman, ambery, larisa, yaoort, vinces, bingle, choicy, heuchs, kolopp, curtin, blazed, potboy, ixtles, meller, monkly, neskhi, barest, atokal, batoka, cumuli, henson, tweaks, loanin, katipo, goleta, scruze, amoral, hathor, bunter, musses, cashoo, beiges, damsel, bleaty, moeken, demast, corset, deasil, pogson, pointy, orbite, plumet, pretio, tilmus, berndt, umbrel, scalps, shapes, scanty, lomein, nontax, vowely, unroot, phoney, pauser, oomiak, jolter, cedere, colony, zaniah, unwise, termes, redtab, tetter, rijken, bibber, zapata, ligule, slaggy, eagres, render, menyie, angora, jigger, outers, router, alupag, jauked, corral, escots, stinks, mecate, rurban, abhors, alltud, faunus, enigme, marsha, oguchi, queuer, fierce, gyrene, anzaas, begeck, insets, skeane, taxmen, cocash, ananas, pedage, downer, besigh, shirty, songle, yuechi, booths, shoals, frills, firman, nacred, cruxes, dixits, dolman, scapes, cathro, toping, finsun, biddle, paries, bettor, antrum, vident, debone, madras, shypoo, uracil, egards, karite, luanda, azonal, sleazo, kelped, perter, nicest, frosty, gooral, upslip, unhang, lucked, webcap, zeekoe, conure, troyer, axunge, breach, seabee, cistae, amuyon, hushel, austin, touter, evoker, klaxon, bildar, monish, crafts, tipcat, shiner, alitur, mousie, eunomy, ifugao, predal, alclad, bedamp, massel, brasil, uploom, godman, soemba, homoeo, abrupt, soloth, cashew, resoak, zebras, spiles, zonked, trocks, garbel, tidbit, tarvia, scarps, escarp, zander, comity, untrig, mulhac, raunch, jarful, troner, invito, sialia, sabirs, bodach, mucksy, audion, gagbit, cockly, lienee, eugene}