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
Examples
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.
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.
Programs
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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 *) -
PARI
isok(k) = #Set(digits(#Str(k^k))) == 1;
Extensions
a(28)-a(42) from Giovanni Resta, Dec 05 2019
Comments