A007521 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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