A120330 Primes not congruent to +- 1, 3, or 4 (mod 13).

2, 5, 7, 11, 13, 19, 31, 37, 41, 47, 59, 67, 71, 73, 83, 89, 97, 109, 137, 149, 151, 163, 167, 193, 197, 223, 227, 229, 239, 241, 271, 281, 293, 307, 317, 331, 349, 353, 359, 379, 383, 397, 401, 409, 421, 431, 449, 457, 461, 463, 479, 487, 499, 509, 541, 557

Offset: 1

Author

Neil Fernandez, Jun 22 2006

Keywords

• easy
• nonn

Comments

This sequence consists of all the primes that are not in A270997. - Bill McEachen, Feb 16 2022

Examples

			37 is prime and congruent to -2 (mod 13), so 37 is a term.
		

Crossrefs

Cf. A038883 (primes congruent to 0, +-1, +-3, +-4 (mod 13)).

Cf. A270997.

Programs

Mathematica

For[a = 1, a < 1001, a++, p = Prime[a]; t = Mod[p, 13]; If[Or[t == 1, t == 3, t == 4, t == 9, t == 10, t == 12] == False, Print[p]]]
Select[Prime[Range[110]],!MemberQ[{1,3,4,9,10,12},Mod[#,13]]&] (* Harvey P. Dale, May 12 2019 *)

PARI

select( {is_A120330(n)=!bittest(5658,n%13)&&isprime(n)}, [0..567]) \\ M. F. Hasler, Feb 17 2022

Formula

A000040 \ A038883 U {13}: Complement of A038883 in the primes, and 13. - M. F. Hasler, Feb 17 2022

Extensions

Corrected by N. J. A. Sloane, May 12 2019 at the suggestion of Harvey P. Dale