A007521 Primes of the form 8k + 5.

5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557, 613, 653, 661, 677, 701, 709, 733, 757, 773, 797, 821, 829, 853, 877, 941, 997, 1013, 1021, 1061, 1069, 1093, 1109, 1117, 1181, 1213

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn
• easy
• nice

Comments

Primes of the form 4x^2 - 4xy + 5y^2 with x and y nonnegative. - T. D. Noe, May 08 2005

Prime numbers 2k+1 with k even such that 2k+1 | 2^k+1. - Hilko Koning, Jan 21 2022

References

• Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A010051.

Subsequence of A004770; see also A045323.

Programs

Haskell

a007521 n = a007521_list !! (n-1)
a007521_list = filter ((== 1). a010051) a004770_list
-- Reinhard Zumkeller, Aug 17 2012

Magma

[p: p in PrimesUpTo(2000) | p mod 8 eq 5]; // Vincenzo Librandi, Jun 26 2014

Mathematica

Select[8Range[0, 160] + 5, PrimeQ]  (* Harvey P. Dale, Apr 22 2011 *)

PARI

list(lim)=select(n->n%8==5,primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011

Python

from sympy import isprime
print(list(filter(isprime, range(5, 1214, 8)))) # Michael S. Branicky, May 13 2021