cp's OEIS Frontend

A342144 Numbers m with integer solution to x^x == (x+1)^(x+1) (mod m) with x > 0.

%I A342144 #19 Mar 08 2021 02:25:13
%S A342144 1,3,5,7,11,13,15,17,19,21,23,29,31,33,35,37,39,41,43,47,49,51,53,55,
%T A342144 57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,
%U A342144 107,109,111,113,115,119,123,127,129,131,133,137,139,141,143,145,147,149,151,155,157,159,161,163,167
%N A342144 Numbers m with integer solution to x^x == (x+1)^(x+1) (mod m) with x > 0.
%C A342144 Some values of m have multiple solutions.
%C A342144 For example, for m = 49, 25^25 == 26^26 (mod 49) and 37^37 == 38^38 (mod 49).
%C A342144 All terms are odd.
%C A342144 First differs from A334420 at a(70) which is 167 for this sequence and 165 for A334420.
%C A342144 First differs from A056911 at a(21) which is 49 for this sequence and 51 for A056911.
%e A342144 3 is a term since 1^1 == 2^2 (mod 3).
%e A342144 5 is a term since 11^11 == 12^12 (mod 5).
%t A342144 seqQ[n_] := AnyTrue[Range[LCM[n, CarmichaelLambda[n]]+1], PowerMod[#, #, n] == PowerMod[# + 1, # + 1, n] &]; Select[Range[145], seqQ]
%Y A342144 Cf. A056911, A084820, A174824, A334420, A338445.
%K A342144 nonn
%O A342144 1,2
%A A342144 _Owen C. Keith_, Mar 01 2021