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Primes of the form 6*k^2 + 1.
4

%I #18 Sep 08 2022 08:45:12

%S 7,97,151,487,601,727,2647,3457,4057,7351,9127,9601,11617,12697,14407,

%T 15607,17497,20887,21601,29401,33751,37447,39367,42337,47527,53017,

%U 54151,71287,77977,80737,84967,95257,102967,110977,126151,142297,151687

%N Primes of the form 6*k^2 + 1.

%C Subset of A002476. See also A121326. The values of k for which 6*k^2 + 1 is prime are 1, 4, 5, 9, 10, 11, 21, 24, 26, 35, 39, 40, 44, 46, 49, 51, 54, 59, 60, 70, 75, 79, 81, 84, 89, 94, 95, 109, 114, 116, 119, 126, 131, 136, 145, 154, ... - _Jonathan Vos Post_, Aug 27 2006

%H Vincenzo Librandi, <a href="/A090687/b090687.txt">Table of n, a(n) for n = 1..5000</a>

%t Select[Table[6n^2+1,{n,0,1000}],PrimeQ] (* _Vincenzo Librandi_, Dec 03 2011 *)

%o (PARI) mx2pmp(n) = { for(x=1,n, y = 6*x^2+1; if(isprime(y),print1(y",")) ) }

%o (Magma) [a: n in [0..600] | IsPrime(a) where a is 6*n^2+1]; // _Vincenzo Librandi_, Dec 03 2011

%Y Cf. A000040, A002476, A090686.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 18 2003

%E Edited by _N. J. A. Sloane_ at the suggestion of _R. J. Mathar_, Apr 14 2008