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

1,1

Comments

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

Links

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

Formula

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

Example

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).

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 *)

Prog

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

Crossrefs

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

Cf. A000720, A040117.

Sequence in context: A226723 A029918 A081842 * A297466 A198267 A298786

Adjacent sequences: A160588 A160589 A160590 * A160592 A160593 A160594

Keyword

nonn

Author

M. F. Hasler, May 21 2009

Status

approved