A121658 Primes neither of the n^2+1 nor n^2+n+1 form.

11, 19, 23, 29, 41, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 199, 223, 227, 229, 233, 239, 251, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349

Offset: 1

Author

Giovanni Teofilatto, Sep 10 2006, Sep 12 2006

Keywords

• easy
• nonn

Comments

Previous name: Primes not equal to [k*(k or k+1 or k+2)] + 1 where k is a natural number.

Primes not of the form n^2 + 1 and n^2 + n + 1 and (n+1)^2. Correct version!!

Primes not contained in A200975 (numbers on the diagonals of Ulam's spiral). - Bob Selcoe, Oct 27 2014

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A200975.

Programs

Mathematica

Select[Prime[Range[100]],NoneTrue[{Sqrt[#-1],(Sqrt[4#-3]-1)/2}, IntegerQ]&] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 23 2015 *)

PARI

lista(nn) = {forprime(p=2, nn, if (!issquare(p-1) && !ispolygonal((p-1)/2, 3), print1(p, ", ")););} \\ Michel Marcus, Oct 28 2014

Extensions

Edited by R. J. Mathar, Aug 02 2008

Data corrected by Bob Selcoe and Michel Marcus, Oct 28 2014