A330193 a(n) is the length of the decimal expansion of A330192(n)^A330192(n).

1, 1, 1, 2, 3, 4, 5, 6, 8, 9, 11, 55, 77, 88, 444, 555, 666, 888, 999, 1111, 4444, 5555, 6666, 9999, 11111, 55555, 99999, 333333, 444444, 666666, 888888, 999999, 1111111, 7777777, 33333333, 88888888, 333333333, 999999999, 5555555555, 222222222222, 44444444444444

Offset: 1

Author

Michel Marcus, Dec 05 2019

Keywords

• nonn
• base

Links

• Giovanni Resta, Table of n, a(n) for n = 1..61
• Cristian Cobeli, DOI^2, arXiv:1911.09003 [math.HO], 2019. See Table 2 p. 8.
• Cristian Cobeli, DOI^2, Romanian Journal Of Pure And Applied Mathematics, Tome LXVI, No. 3-4, 2021.

Crossrefs

Cf. A010785 (repdigits), A000312 (n^n), A055642, A066022, A330192.

Programs

Mathematica

Flatten@ Reap[Sow[1]; Do[v = d (10^nd - 1)/9; s = Solve[v-1 <= x Log10[x] < v, x, Integers]; If[s != {}, Sow[v /. s]], {nd, 15}, {d, 9}]][[2, 1]] (* Giovanni Resta, Dec 05 2019 *)

Formula

a(n) = A066022(A330192(n)).

a(n) = A055642(A330192(n)^A330192(n)).

Extensions

a(28)-a(41) from Giovanni Resta, Dec 05 2019