OFFSET
1,1
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
Wei-Liang Sun, Cyclotomic Matrices and Power Difference Sets, arXiv:2511.13613 [math.RA], 2025. See p. 20, Theorem 5.13.
MATHEMATICA
Select[Table[8n^2 - 1, {n, 9000}], PrimeQ] (* Alonso del Arte, Mar 27 2011 *)
PROG
(PARI) mx2pmp(n) = { for(x=1, n, my(y = 8*x^2-1); if(isprime(y), print1(y, ", ")) ) }
(Magma) [8*n^2-1: n in [1..95] | IsPrime(8*n^2-1)]; // Bruno Berselli, Mar 28 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 18 2003
STATUS
approved