A176549 - OEIS

%I #26 Sep 08 2022 08:45:52

%S 37,109,541,757,1009,1297,1621,2377,6841,7561,8317,9109,11701,12637,

%T 15661,16741,19009,23977,25309,28081,34057,38917,40609,42337,44101,

%U 47737,51517,55441,57457,59509,65881,70309,72577,82009,84457,99901

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

%C Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

%C 2*a(n) + 7 is a square. - _Vincenzo Librandi_, Apr 09 2015

%H Vincenzo Librandi, <a href="/A176549/b176549.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Table[2 n^2 + 6 n + 1, {n, 2000}], PrimeQ] (* _Vincenzo Librandi_, Jul 26 2012 *)

%o (Magma) [a: n in [0..300] | IsPrime(a) where a is 2*n^2+6*n+1]; // _Vincenzo Librandi_, Jul 26 2012

%Y Primes in A059993.

%Y Subsequence of A093838.

%Y Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): this sequence (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), A217621 (k=21).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Apr 20 2010

%E Removed an obviously incorrect part of the definition - _R. J. Mathar_, Apr 21 2010