A160591 Indices of primes congruent to 5 modulo 12.

3, 7, 10, 13, 16, 24, 26, 30, 33, 35, 40, 45, 51, 55, 57, 60, 62, 66, 71, 77, 79, 87, 89, 97, 98, 102, 104, 108, 113, 116, 119, 123, 126, 135, 137, 139, 140, 142, 148, 152, 158, 160, 162, 165, 170, 176, 178, 184, 186, 194, 196, 199, 201, 206, 209, 212, 218, 220, 223

Offset: 1

Author

M. F. Hasler, May 21 2009

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021

Examples

			a(1) = 3 since the 3rd prime, A000040(3) = 5, is the first one to be equal to 5 (mod 12).
a(2) = 7 since the 7th prime, A000040(7) = 17, is the second one to be equal to 5 (mod 12).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A116602 lists the even terms of this sequence, divided by 2.

Cf. A000720, A040117.

Programs

Maple

res:= NULL: p:= 2:
for m from 2 to 1000 do
  p:= nextprime(p);
  if p mod 12 = 5 then res:= res, m fi;
od:
res; # Robert Israel, Dec 26 2016

Mathematica

Select[{#, Prime[#]}& /@ Range[500], Mod[#[[2]], 12] == 5&] [[All, 1]] (* Jean-François Alcover, Mar 23 2019 *)
Select[Range[300],Mod[Prime[#],12]==5&] (* Harvey P. Dale, Mar 18 2023 *)

PARI

for(n=1,999, prime(n)%12==5 & print1(n","))

Formula

a(n) = A000720(A040117(n)).