A045326 - OEIS

%I #40 Jun 23 2023 10:03:21

%S 2,3,7,11,19,23,31,43,47,59,67,71,79,83,103,107,127,131,139,151,163,

%T 167,179,191,199,211,223,227,239,251,263,271,283,307,311,331,347,359,

%U 367,379,383,419,431,439,443,463,467,479,487,491,499,503,523,547,563,571,587,599,607,619

%N Primes congruent to {2, 3} mod 4.

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

%C Primes not in A002144. - _Juri-Stepan Gerasimov_, Oct 16 2010

%H Ray Chandler, <a href="/A045326/b045326.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)

%F a(n) ~ 2n log n. - _Charles R Greathouse IV_, Dec 11 2016

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

%o (Magma) [p: p in PrimesUpTo(740) | p mod 4 in [2,3]] // _Vincenzo Librandi_, Dec 18 2010

%o (PARI) is(n)=n%4>1 && isprime(n) \\ _Charles R Greathouse IV_, Dec 11 2016

%o (Python)

%o from itertools import count, islice

%o from sympy import prime

%o def A045326_gen(): # generator of terms

%o     return filter(lambda n:n>>1&1,map(prime,count(1)))

%o A045326_list = list(islice(A045326_gen(),20)) # _Chai Wah Wu_, Jun 23 2023

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_