cp's OEIS Frontend

A277859 Least k > 1 such that 1^(k-1) + 2^(k-1) + 3^(k-1) + … + (k-1)^(k-1) - n == 0 (mod k).

%I A277859 #10 Jun 02 2025 12:19:53
%S A277859 2,3,2,4,2,7,2,3,2,11,2,4,2,3,2,4,2,19,2,3,2,23,2,4,2,3,2,4,2,31,2,3,
%T A277859 2,5,2,4,2,3,2,4,2,9,2,3,2,47,2,4,2,3,2,4,2,5,2,3,2,59,2,4,2,3,2,4,2,
%U A277859 45,2,3,2,15,2,4,2,3,2,4,2,9,2,3,2,83,2,4,2
%N A277859 Least k > 1 such that 1^(k-1) + 2^(k-1) + 3^(k-1) + … + (k-1)^(k-1) - n == 0 (mod k).
%C A277859 a(2*n-1) = 2.
%C A277859 a(n) = n + 1 for some prime n + 1 congruent to {2, 3} mod 4.
%H A277859 Paolo P. Lava, <a href="/A277859/b277859.txt">Table of n, a(n) for n = 1..1000</a>
%e A277859 a(8) = 3 because:
%e A277859 1^(2-1) - 8 = -7 but -7 mod 2 = 1;
%e A277859 1^(3-1) + 2^(3-1) - 8 = -3 and  -3 mod 3 = 0;
%p A277859 P:=proc(q) local j,k,n; for n from 1 to q do for k from 2 to q do
%p A277859 if (add(j^(k-1),j=1..k-1)-n) mod k=0 then print(k); break; fi; od; od; end: P(10^3);
%Y A277859 Cf. A045326, A191677.
%K A277859 nonn,easy
%O A277859 1,1
%A A277859 _Paolo P. Lava_, Nov 02 2016