A122430 Primes of the form 1+2*n+3*n^2.

17, 457, 617, 1009, 1777, 2081, 3137, 4409, 5897, 9521, 11657, 14009, 24481, 25577, 29009, 39217, 43441, 47881, 49409, 62497, 67801, 75209, 81017, 85009, 87041, 93281, 97561, 104161, 110977, 120401, 132721, 135257, 140401, 159161, 182041

Offset: 1

Author

Zak Seidov, Oct 20 2006

Keywords

• nonn

Comments

3*a(n)-2 is a square (of the form (3*k+1)^2). - Vincenzo Librandi, Mar 15 2013

Also primes which are the sum of 2 consecutive pentagonal numbers (A000326). - Vicente Izquierdo Gomez, Aug 13 2017

Links

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

Crossrefs

Cf. A086285 (numbers n such that 1+2n+3n^2 is prime).

Subsequence of A056109.

Programs

Magma

[a: n in [1..300] | IsPrime(a) where a is 1+2*n+3*n^2]; // Vincenzo Librandi, Mar 15 2013

Mathematica

Select[Table[1 + 2 n + 3 n^2, {n, 500}], PrimeQ] (* Vincenzo Librandi, Mar 15 2013 *)

PARI

is(n)=isprime(n) && issquare(3*n-2,&n) && n%3==1 \\ Charles R Greathouse IV, Sep 23 2013