A176549 Primes of the form 2*n^2+6*n+1.

37, 109, 541, 757, 1009, 1297, 1621, 2377, 6841, 7561, 8317, 9109, 11701, 12637, 15661, 16741, 19009, 23977, 25309, 28081, 34057, 38917, 40609, 42337, 44101, 47737, 51517, 55441, 57457, 59509, 65881, 70309, 72577, 82009, 84457, 99901

Offset: 1

Author

Vincenzo Librandi, Apr 20 2010

Keywords

• nonn
• easy

Comments

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

2*a(n) + 7 is a square. - Vincenzo Librandi, Apr 09 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Primes in A059993.

Subsequence of A093838.

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).

Programs

Magma

[a: n in [0..300] | IsPrime(a) where a is 2*n^2+6*n+1]; // Vincenzo Librandi, Jul 26 2012

Mathematica

Select[Table[2 n^2 + 6 n + 1, {n, 2000}], PrimeQ] (* Vincenzo Librandi, Jul 26 2012 *)

Extensions

Removed an obviously incorrect part of the definition - R. J. Mathar, Apr 21 2010