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%I #17 Jun 28 2024 22:27:08
%S 5,51,751,10001,100001,1000001,10000001,100000001,1000000001
%N Smallest integer m > 1 such that m == m^m (mod 10^(len(m) + n)), where len(m) is the number of digits of m.
%C By definition, this sequence is a subsequence of A082576.
%C It is not known if a(n) = 10^(n + 1) + 1 holds for all n >= 3.
%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>
%e a(2) = 751 since m = 751 is the smallest integer satisfying m == m^m (mod 10^(len(m) + 2)), given the fact that 751 is a 3-digit number and 751^751 == 500751 (mod 10^6) and thus 751^751 == 751 (mod 10^(3 + 2)).
%o (PARI) a(n) = my(im); for (len_m = 1, oo, if (len_m==1, im=2, im=10^(len_m - 1)); for (m = im, 10^len_m - 1, if (m == Mod(m, 10^(len_m + n))^m, return(m)))); \\ _Michel Marcus_, Jun 03 2024
%Y Cf. A000533, A055642, A082576, A373205, A373206.
%K nonn,base,more
%O 0,1
%A _Marco Ripà_, Jun 02 2024
%E a(7)-a(8) from _Michel Marcus_, Jun 03 2024
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