%I #25 Nov 26 2025 12:12:20

%S 7,31,71,127,199,647,967,1151,1567,2311,2591,2887,3527,4231,4999,5407,

%T 6271,7687,8191,11551,12799,16927,19207,20807,23327,25087,27847,31751,

%U 34847,35911,39199,47431,49927,51199,53791,59167,63367,69191,70687

%N Primes of the form 8*k^2 - 1.

%C 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.

%H Vincenzo Librandi, <a href="/A090684/b090684.txt">Table of n, a(n) for n = 1..10000</a>

%H Wei-Liang Sun, <a href="https://arxiv.org/abs/2511.13613">Cyclotomic Matrices and Power Difference Sets</a>, arXiv:2511.13613 [math.RA], 2025. See p. 20, Theorem 5.13.

%t Select[Table[8n^2 - 1, {n, 9000}], PrimeQ] (* _Alonso del Arte_, Mar 27 2011 *)

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

%o (Magma) [8*n^2-1: n in [1..95] | IsPrime(8*n^2-1)]; // _Bruno Berselli_, Mar 28 2011

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 18 2003