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

1,1

Comments

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

Links

Table of n, a(n) for n=1..56.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Cf. A270997.

Sequence in context: A098170 A256396 A291280 * A023216 A079449 A236071

Adjacent sequences: A120327 A120328 A120329 * A120331 A120332 A120333

Keyword

easy,nonn

Author

Neil Fernandez, Jun 22 2006

Extensions

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

Status

approved