A007521 Primes of the form 8k + 5. (Formerly M3828)

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

1,1

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].

Mathematica

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

Prog

(PARI) list(lim)=select(n->n%8==5, primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011
(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
(Python)
from sympy import isprime
print(list(filter(isprime, range(5, 1214, 8)))) # Michael S. Branicky, May 13 2021

Crossrefs

Cf. A010051.

Subsequence of A004770; see also A045323.

Sequence in context: A347836 A100877 A261580 * A294919 A213050 A216822

Adjacent sequences: A007518 A007519 A007520 * A007522 A007523 A007524

Keyword

nonn,easy,nice

Author

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

Status

approved