A156226 Primes of the form 9*n^2 + 1.

37, 577, 1297, 2917, 4357, 7057, 8101, 14401, 15877, 22501, 24337, 32401, 41617, 44101, 57601, 69697, 72901, 90001, 93637, 147457, 156817, 176401, 197137, 224677, 324901, 331777, 352837, 404497, 427717, 476101, 484417, 509797, 562501

Offset: 1

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 06 2009

Keywords

• nonn

Comments

9*n^2 + 1 can be a prime only for n's of the form n=10m or n=10m+-2.

Primes in this sequence must end with 1 or 7 and will have to be 1 modulo 30 or 7 modulo 30.

Examples

			a(5) = 4357 = 9*22^2 + 1.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1400

Crossrefs

Intersection of A002496 and A016777.

Programs

Magma

[a: n in [0..250] | IsPrime(a) where a is 9*n^2+1]; // Vincenzo Librandi, Dec 13 2010

Maple

A156226:=n->`if`(isprime(9*n^2+1),9*n^2+1,NULL): seq(A156226(n), n=1..500); # Wesley Ivan Hurt, Sep 19 2014

Mathematica

Union[Select[9#^2+1&/@Flatten[Table[{10m,10m+2,10m-2},{m,0,50}]],PrimeQ]] (* Harvey P. Dale, Dec 16 2010 *)
Select[Table[9 n^2 + 1, {n, 0, 2000}], PrimeQ] (* Vincenzo Librandi, Sep 20 2014 *)

PARI

for(n=1,10^3,if(isprime(9*n^2+1),print1(9*n^2+1,", "))) \\ Derek Orr, Sep 19 2014

Extensions

Corrected, extended, comments added by Rick L. Shepherd and Zak Seidov, Feb 08 2009