A090684 Primes of the form 8*n^2 - 1.

7, 31, 71, 127, 199, 647, 967, 1151, 1567, 2311, 2591, 2887, 3527, 4231, 4999, 5407, 6271, 7687, 8191, 11551, 12799, 16927, 19207, 20807, 23327, 25087, 27847, 31751, 34847, 35911, 39199, 47431, 49927, 51199, 53791, 59167, 63367, 69191, 70687

Offset: 1

Author

Cino Hilliard, Dec 18 2003

Keywords

• easy
• nonn

Comments

In the odd number variant of the Ulam spiral, unimpeded by even numbers, prime numbers can line up in horizontal and vertical lines. But there are still noticeable diagonal lines of primes, and these primes fall on one such diagonal.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Programs

Magma

[8*n^2-1: n in [1..95] | IsPrime(8*n^2-1)];  // Bruno Berselli, Mar 28 2011

Mathematica

Select[Table[8n^2 - 1, {n, 9000}], PrimeQ] (* Alonso del Arte, Mar 27 2011 *)

PARI

mx2pmp(n,m) = { for(x=1,n, y = 8*x^2-1; if(isprime(y),print1(y",")) ) }