A212876 Numbers of the form n^2+1 such that 3^(m+3)==9 (mod m) where m=n^4-1.

5, 17, 37, 101, 257, 1297, 4357, 14401, 44101, 65537, 828101, 933157, 8122501, 8386817, 12362257, 41990401, 121220101, 157402117, 223502501, 318622501, 378146917, 506700101, 684345601, 702038017

Offset: 1

Author

Alzhekeyev Ascar M, May 29 2012

Keywords

• nonn

Comments

All the known values of the sequence are prime (for a(n)<10^20). - Charles R Greathouse IV, Jun 07 2012

The values of n+1 are prime or composite 121, 11011, 108781, 170431...

All composite n+1 == 1 (mod 3) ???

Examples

			Let n = 10. Then m = n^4-1 = 9999. 3^10002 == 9 (mod 9999), so n^2+1 = 101 is a member of the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..3556

Programs

PARI

v=List();for(n=2,1e6,m=n^4-1;if(Mod(3,m)^(m+3)==9, listput(v, n^2+1))); Vec(v) \\ Charles R Greathouse IV, May 29 2012