This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373386 #17 Jun 28 2024 22:27:08 %S A373386 5,51,751,10001,100001,1000001,10000001,100000001,1000000001 %N A373386 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 A373386 By definition, this sequence is a subsequence of A082576. %C A373386 It is not known if a(n) = 10^(n + 1) + 1 holds for all n >= 3. %H A373386 <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a> %e A373386 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 A373386 (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 A373386 Cf. A000533, A055642, A082576, A373205, A373206. %K A373386 nonn,base,more %O A373386 0,1 %A A373386 _Marco Ripà_, Jun 02 2024 %E A373386 a(7)-a(8) from _Michel Marcus_, Jun 03 2024