A212912 Numbers k such that 3^(m+3) == 9 (mod m) where m = (k-1)^2 - 1.

3, 5, 7, 11, 17, 37, 47, 53, 67, 97, 101, 121, 211, 257, 367, 379, 457, 617, 911, 1091, 1237, 1297, 1361, 1549, 2003, 2557, 2851, 2897, 3517, 3733, 4201, 4357, 5209, 6481, 7621, 8461, 8647, 8689, 10253, 10457, 10631, 11953, 13729, 14401, 14951, 17431, 17837

Offset: 1

Author

Alzhekeyev Ascar M, May 30 2012

Keywords

• nonn

Comments

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)?

Programs

Mathematica

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

PARI

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

Extensions

More terms from Harvey P. Dale, Dec 07 2019