The picture shows the descriptive 3789*10^973-1 expanded by Mathematica into its actual 977-digit length. The number is a(8) in Sloane's A001273, where a(0) - a(7) are 1, 10, 13, 23, 19, 7, 356, and 78999. The large a(8) was described by Jud McCranie in 1994. Yesterday, I extended this sequence all the way to a(12) using a technique I developed to extend a related sequence, A176762. Unfortunately, my technique requires the use of modular arithmetic which I could do only for deriving a(9) and a(10). To derive a(11) and a(12), I had to resort to borrowing the modular arithmetic from an online document that also calculates these terms up to a(12) — so it looks a little like I'm cheating, except that I did develop my method independently (though not at all rigorously) and it is possible for me to document that (through my exchanges on the SeqFan and MathFun mailing lists).

a(7)  =    79*10^((a(6) -113)/81)-1

a(8)  =  3789*10^((a(7) -186)/81)-1

a(9)  = 78889*10^((a(8) -305)/81)-1

a(9) can be described thus: the five digits 78888 followed by 467777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777774 nines. The number was first specified by Warut Roonguthai for UPINT3 (section E34).

a(10) =   259*10^((a(9) - 93)/81)-1

a(11) =   179*10^((a(10)-114)/81)-1

a(12) =    47*10^((a(11)- 52)/81)-1

A creative sequence fanatic might see here two sequences: {79, 3789, 78889, 259, 179, 47, ...} and {113, 186, 305, 93, 114, 52, ...}. But both of these sequences are simple table-lookups from the values of {a(6), a(7), ... a(11)} mod 81, so the better sequence is {32, 24, 62, 12, 33, 52, ...}. It strikes me that a good understanding of modular arithmetic would allow someone to extend this latter sequence ad nauseam.