A045323 Primes congruent to {1, 2, 3, 7} (mod 8).

2, 3, 7, 11, 17, 19, 23, 31, 41, 43, 47, 59, 67, 71, 73, 79, 83, 89, 97, 103, 107, 113, 127, 131, 137, 139, 151, 163, 167, 179, 191, 193, 199, 211, 223, 227, 233, 239, 241, 251, 257, 263, 271, 281, 283, 307, 311

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers x such that x^4 = 4 has a solution mod p.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Crossrefs

Cf. A000040, A010051.

Subsequence of A004776; see also A007521.

Programs

Haskell

a045323 n = a045323_list !! (n-1)
a045323_list = filter ((== 1). a010051) a004776_list
-- Reinhard Zumkeller, Aug 17 2012

Magma

[ p: p in PrimesUpTo(400) | p mod 8 in {1, 2, 3, 7} ]; // Vincenzo Librandi, Aug 07 2012

Mathematica

Select[Prime[Range[300]],MemberQ[{1,2,3,7},Mod[#,8]]&] (* Vincenzo Librandi, Aug 07 2012 *)