A330192 Integers k such that the length of decimal expansion of k^k is a repdigit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 35, 46, 51, 194, 234, 273, 349, 386, 423, 1411, 1717, 2017, 2889, 3173, 13455, 22933, 68896, 89733, 130334, 169949, 189481, 208861, 1273968, 4977354, 12523569, 43631177, 123579653, 631296394, 21506946847, 3541615362849, 8590606646469

Offset

1,3

Comments

Integers k such that A066022(k) belongs to A010785.

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. 7.

Cristian Cobeli, DOI^2, Romanian Journal Of Pure And Applied Mathematics, Tome LXVI, No. 3-4, 2021.

Example

For k=1 to 9, k^k has k digits, that is, A066022(k) is a repdigit.
k=631296394 is a term since k^k has 5555555555 digits. See Cobeli link.

Mathematica

Flatten@ Reap[Sow[0]; Do[v = d (10^nd-1)/9; s = Solve[v-1 <= x Log10[x] < v, x, Integers]; If[s != {}, Sow[x /. s]], {nd, 15}, {d, 9}]][[2, 1]] (* Giovanni Resta, Dec 05 2019 *)

Prog

(PARI) isok(k) = #Set(digits(#Str(k^k))) == 1;

Crossrefs

Cf. A010785 (repdigits), A000312 (n^n), A066022 (number of digits of n^n), A330193.

Sequence in context: A004850 A260096 A141709 * A062683 A363765 A137857

Adjacent sequences: A330189 A330190 A330191 * A330193 A330194 A330195

Keyword

nonn,base

Author

Michel Marcus, Dec 05 2019

Extensions

a(28)-a(42) from Giovanni Resta, Dec 05 2019

Status

approved