A257483 Primes p such that (p mod 8) = (p mod 27).

2, 3, 5, 7, 223, 433, 439, 653, 1087, 1297, 1301, 1303, 1733, 1949, 1951, 2161, 2377, 2381, 2383, 2593, 3457, 3461, 3463, 3673, 3677, 3889, 4111, 4327, 4759, 4969, 4973, 5189, 5407, 5623, 5839, 6053, 6269, 6271, 6481, 6701, 6703, 6917, 7129, 7349, 7351, 7561

Offset: 1

Author

Zak Seidov, Apr 26 2015

Keywords

• nonn
• easy

Comments

a(n) is 2, 3 or of the form 216k + r where r is in {1, 5, 7} - David A. Corneth, May 26 2015

Examples

			223 == 7 (mod 8) == 7 (mod 27),  433 == 1 (mod 8) == 1 (mod 27).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A039706, A242125, A257482.

Programs

Magma

[p: p in PrimesUpTo(8000) | p mod 8  eq  p mod 27]; // Vincenzo Librandi, Apr 28 2015

Maple

select(isprime,[2,3,seq(seq(216*k+r,r=[1,5,7]),k=0..1000)]); # Robert Israel, May 26 2015

Mathematica

Select[Prime@ Range@ 1000, Mod[#, 8] == Mod[#, 27] &] (* Michael De Vlieger, Apr 27 2015 *)

PARI

is(n)=my(k=n%216); (k==1||k==5||k==7) && isprime(n) \\ Charles R Greathouse IV, May 26 2015

Formula

a(n) = A000040(A257482(n)).

a(n) ~ 24n log n. - Charles R Greathouse IV, May 26 2015