cp's OEIS Frontend

A373901 Numbers m such that (m - k)^k modulo m is not equal to positive k <= m.

%I A373901 #43 Jul 22 2024 15:34:30
%S A373901 1,3,4,8,11,16,17,19,32,43,59,64,67,83,107,128,131,137,179,227,251,
%T A373901 256,347,467,512,523,563,587,683,691,787,907,971,977,1019,1024,1097,
%U A373901 1187,1259,1283,1307,1459,1523,1579,1619,1627,1699,1723,1787,1867,1907,1931,1987,2027,2048
%N A373901 Numbers m such that (m - k)^k modulo m is not equal to positive k <= m.
%C A373901 The odd composite and the even composite terms of this sequence are respectively 3353, 4213, 9233, 10813, ... and all and only powers of 2 >= 4.
%e A373901 1 is in this sequence because (1-1)^1 mod 1 = 0 != 1.
%e A373901 3 is in this sequence because
%e A373901   (3-1)^1 mod 3 = 2 != 1,
%e A373901   (3-2)^2 mod 3 = 1 != 2,
%e A373901   (3-3)^3 mod 3 = 0 != 3.
%o A373901 (Magma) [m : m in [1..2^11] | #[k: k in [1..m] | (m-k)^k mod m eq k] eq 0];
%o A373901 (PARI) isok(m) = for (k=1, m, if ((m - k)^k % m == k, return (0))); return(1); \\ _Michel Marcus_, Jun 30 2024
%Y A373901 Supersequence of A151821.
%K A373901 nonn
%O A373901 1,2
%A A373901 _Juri-Stepan Gerasimov_, Jun 22 2024