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Primes of the form 9*n^2 + 1.
3

%I #22 Sep 08 2022 08:45:41

%S 37,577,1297,2917,4357,7057,8101,14401,15877,22501,24337,32401,41617,

%T 44101,57601,69697,72901,90001,93637,147457,156817,176401,197137,

%U 224677,324901,331777,352837,404497,427717,476101,484417,509797,562501

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

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

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

%H Vincenzo Librandi, <a href="/A156226/b156226.txt">Table of n, a(n) for n = 1..1400</a>

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

%p 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

%t Union[Select[9#^2+1&/@Flatten[Table[{10m,10m+2,10m-2},{m,0,50}]],PrimeQ]] (* _Harvey P. Dale_, Dec 16 2010 *)

%t Select[Table[9 n^2 + 1, {n, 0, 2000}], PrimeQ] (* _Vincenzo Librandi_, Sep 20 2014 *)

%o (Magma) [a: n in [0..250] | IsPrime(a) where a is 9*n^2+1]; // _Vincenzo Librandi_, Dec 13 2010

%o (PARI) for(n=1,10^3,if(isprime(9*n^2+1),print1(9*n^2+1,", "))) \\ _Derek Orr_, Sep 19 2014

%Y Intersection of A002496 and A016777.

%K nonn

%O 1,1

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

%E Corrected, extended, comments added by _Rick L. Shepherd_ and _Zak Seidov_, Feb 08 2009