A188382 Primes of the form 8*n^2 + 2*n + 1.

11, 37, 79, 137, 211, 821, 991, 1597, 1831, 2081, 2347, 2927, 3571, 3917, 4657, 5051, 6329, 8779, 9871, 11027, 14197, 14879, 17021, 20101, 21737, 26107, 27967, 28921, 33931, 34981, 39341, 40471, 41617, 50087, 51361, 59341

Offset: 1

Author

Alonso del Arte, Mar 29 2011

Keywords

• nonn
• easy

Comments

In a variant of the Ulam spiral with only odd numbers, prime numbers can line up in horizontal or vertical lines rather than diagonal lines. These primes are on one such horizontal (or vertical) line.

Primes in A188135. Primes in the sequence found by reading the line from 1, in the direction 1, 11, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011

Equivalently, primes of the form 2*n^2+n+1. - N. J. A. Sloane, Nov 08 2014

Links

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

Crossrefs

Cf. A090684, A187677.

Programs

Magma

[ a: n in [0..250] | IsPrime(a) where a is 8*n^2 + 2*n + 1 ]; // Vincenzo Librandi, Apr 05 2011

Maple

select(isprime,[seq(8*n^2+2*n+1,n=0..86)]); # Peter Luschny, Aug 22 2011

Mathematica

Select[Table[8n^2 + 2n + 1, {n, 100}], PrimeQ]

PARI

select(isprime, vector(1000,n,8*n^2+2*n+1)) \\ Charles R Greathouse IV, Jun 14 2011