A160594 Indices of primes congruent to 1 modulo 12.

6, 12, 18, 21, 25, 29, 37, 42, 44, 50, 53, 59, 65, 68, 70, 74, 78, 80, 82, 84, 88, 100, 106, 110, 112, 121, 122, 127, 130, 134, 136, 145, 147, 151, 159, 168, 169, 172, 174, 180, 183, 187, 189, 191, 197, 198, 203, 204, 211, 216, 221, 226, 231, 237, 244, 251, 254

Offset: 1

Author

M. F. Hasler, May 22 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) = 6 since the 6th prime, A000040(6) = 13, is the first one to be equal to 1 (mod 12).
a(2) = 12 since the 12th prime, A000040(12) = 37, is the second one to be equal to 1 (mod 12).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

A116614 lists the even terms of this sequence, divided by 2.

Cf. A000720, A068228.

Programs

Mathematica

PrimePi/@Select[Range[1,1701,12],PrimeQ] (* Harvey P. Dale, Nov 28 2011 *)

PARI

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

Formula

a(n) = A000720(A068228(n)).