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

%I A330192 #19 Apr 13 2022 13:01:45
%S A330192 0,1,2,3,4,5,6,7,8,9,10,35,46,51,194,234,273,349,386,423,1411,1717,
%T A330192 2017,2889,3173,13455,22933,68896,89733,130334,169949,189481,208861,
%U A330192 1273968,4977354,12523569,43631177,123579653,631296394,21506946847,3541615362849,8590606646469
%N A330192 Integers k such that the length of decimal expansion of k^k is a repdigit.
%C A330192 Integers k such that A066022(k) belongs to A010785.
%H A330192 Giovanni Resta, <a href="/A330192/b330192.txt">Table of n, a(n) for n = 1..61</a>
%H A330192 Cristian Cobeli, <a href="https://arxiv.org/abs/1911.09003">DOI^2</a>, arXiv:1911.09003 [math.HO], 2019. See Table 2 p. 7.
%H A330192 Cristian Cobeli, <a href="http://imar.ro/journals/Revue_Mathematique/pdfs/2021/3-4/8.pdf">DOI^2</a>, Romanian Journal Of Pure And Applied Mathematics, Tome LXVI,  No. 3-4, 2021.
%e A330192 For k=1 to 9, k^k has k digits, that is, A066022(k) is a repdigit.
%e A330192 k=631296394 is a term since k^k has 5555555555 digits. See Cobeli link.
%t A330192 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 *)
%o A330192 (PARI) isok(k) = #Set(digits(#Str(k^k))) == 1;
%Y A330192 Cf. A010785 (repdigits), A000312 (n^n), A066022 (number of digits of n^n), A330193.
%K A330192 nonn,base
%O A330192 1,3
%A A330192 _Michel Marcus_, Dec 05 2019
%E A330192 a(28)-a(42) from _Giovanni Resta_, Dec 05 2019