A073337 Primes of the form 4*k^2 - 10*k + 7 with k positive.

3, 13, 31, 241, 307, 463, 757, 1123, 1723, 3307, 3541, 4831, 5113, 5701, 6007, 8011, 9901, 10303, 11131, 12433, 13807, 14281, 17293, 20023, 20593, 21757, 23563, 24181, 26083, 28057, 30103, 35911, 41413, 43891, 46441, 53593, 60271, 78121, 82657, 86143, 95791, 108571, 123553, 127807, 136531, 145543, 147073, 156421

Offset: 1

Author

Zak Seidov, Aug 25 2002

Keywords

• easy
• nonn

Comments

Primes of the form k^2 + k + 1 with k odd and positive. - Peter Munn, Jan 27 2018

Primes of the form A000217(2*k) + A000217(2*k+2). - J. M. Bergot, May 09 2018

Examples

			3 is a term because for k=2, 4*k^2 - 10*k + 7 = 3 a prime.
7 is not a term because 7 can only be obtained with k=0 or k=5/2.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000217, A054554, A073338, A168026.

Subset of A002383.

Programs

GAP

Filtered(List([2..300],n->4*n^2-10*n+7),IsPrime); # Muniru A Asiru, Apr 15 2018

Magma

[a: n in [1..400] | IsPrime(a) where a is 4*n^2 - 10*n + 7]; // Vincenzo Librandi, Dec 23 2019

Maple

select(isprime, [seq(4*n^2-10*n+7 ,n=2..300)]); # Muniru A Asiru, Apr 15 2018

Mathematica

Select[Table[4 n^2 - 10 n + 7, {n, 1, 200}], PrimeQ] (* Vincenzo Librandi, Dec 23 2019 *)

PARI

select(isprime,vector(300,k,4*k^2 - 10*k + 7)) \\ Joerg Arndt, Feb 28 2018

Formula

a(n) = A054554(A073338(n)). - Elmo R. Oliveira, Apr 20 2025

Extensions

Edited by Dean Hickerson, Aug 28 2002

a(1)=7 inserted and typo in Mathematica code corrected by Vincenzo Librandi, Dec 09 2011

Incorrect term 7 removed by Joerg Arndt, Feb 28 2018