A221902 Primes of the form 2*n^2 + 10*n + 3.

31, 103, 211, 751, 1291, 2371, 2803, 3271, 5503, 6151, 8311, 9103, 9931, 17851, 23971, 25303, 32503, 42331, 49603, 51511, 68071, 82003, 94603, 97231, 105331, 119551, 122503, 137803, 157351, 167611, 171103, 174631, 192811, 204151

Offset: 1

Author

Vincenzo Librandi, Jan 31 2013

Keywords

• nonn
• easy

Comments

Conjecture: After the first term, 2^a(n)-1 is not prime; in other words, these primes (except 31) are included in A054723.

2*a(n) + 19 is a square. - Vincenzo Librandi, Apr 10 2015

Links

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

Crossrefs

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (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).

Cf. A054723 (Prime exponents of nonprime Mersenne numbers).

Programs

Magma

[a: n in [1..500] | IsPrime(a) where a is 2*n^2 + 10*n + 3];

Mathematica

Select[Table[2 n^2 + 10 n + 3,{n, 500}],PrimeQ]