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

%I #21 Feb 19 2022 10:23:24

%S 2,5,7,11,13,19,31,37,41,47,59,67,71,73,83,89,97,109,137,149,151,163,

%T 167,193,197,223,227,229,239,241,271,281,293,307,317,331,349,353,359,

%U 379,383,397,401,409,421,431,449,457,461,463,479,487,499,509,541,557

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

%C This sequence consists of all the primes that are not in A270997. - _Bill McEachen_, Feb 16 2022

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

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

%t 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]]]

%t Select[Prime[Range[110]],!MemberQ[{1,3,4,9,10,12},Mod[#,13]]&] (* _Harvey P. Dale_, May 12 2019 *)

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

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

%Y Cf. A270997.

%K easy,nonn

%O 1,1

%A _Neil Fernandez_, Jun 22 2006

%E Corrected by _N. J. A. Sloane_, May 12 2019 at the suggestion of _Harvey P. Dale_