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.

5, 51, 751, 10001, 100001, 1000001, 10000001, 100000001, 1000000001

Offset: 0

Author

Marco Ripà, Jun 02 2024

Keywords

• nonn
• base
• more

Comments

By definition, this sequence is a subsequence of A082576.

It is not known if a(n) = 10^(n + 1) + 1 holds for all n >= 3.

Examples

			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)).
		

Links

• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A000533, A055642, A082576, A373205, A373206.

Programs

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

Extensions

a(7)-a(8) from Michel Marcus, Jun 03 2024