A212912 - OEIS

%I #14 Feb 09 2021 01:56:48

%S 3,5,7,11,17,37,47,53,67,97,101,121,211,257,367,379,457,617,911,1091,

%T 1237,1297,1361,1549,2003,2557,2851,2897,3517,3733,4201,4357,5209,

%U 6481,7621,8461,8647,8689,10253,10457,10631,11953,13729,14401,14951,17431,17837

%N Numbers k such that 3^(m+3) == 9 (mod m) where m = (k-1)^2 - 1.

%C Composites begin: 121, 108781, 155365, 267547, 2774521, 3166087, 3225601, 4907701, 8341201, 10712857, 11035921, 13216141, 17559829, 21708961, 29641921, 31116241, 31150351, ... are all composite terms congruent to 1 (mod 3)?

%t Join[{3},Select[Range[4,20000],PowerMod[3,(#-1)^2+2,(#-1)^2-1]==9&]] (* _Harvey P. Dale_, Dec 07 2019 *)

%o (PARI) for(n=2, 1000, m=n^2-1; if(Mod(3, m)^(m+3)==9, print(n+1)));

%K nonn

%O 1,1

%A _Alzhekeyev Ascar M_, May 30 2012

%E More terms from _Harvey P. Dale_, Dec 07 2019