A045326 Primes congruent to {2, 3} mod 4.

2, 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571, 587, 599, 607, 619

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Apart from initial term 2, same as A002145 (primes of the form 4k+3).

Primes not in A002144. - Juri-Stepan Gerasimov, Oct 16 2010

Links

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

Programs

Magma

[p: p in PrimesUpTo(740) | p mod 4 in [2,3]] // Vincenzo Librandi, Dec 18 2010

Mathematica

Select[Prime[Range[120]], MemberQ[{2, 3}, Mod[#, 4]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)

PARI

is(n)=n%4>1 && isprime(n) \\ Charles R Greathouse IV, Dec 11 2016

Python

from itertools import count, islice
from sympy import prime
def A045326_gen(): # generator of terms
    return filter(lambda n:n>>1&1,map(prime,count(1)))
A045326_list = list(islice(A045326_gen(),20)) # Chai Wah Wu, Jun 23 2023

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Dec 11 2016