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

1,1

Comments

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

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

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

Cf. A000720, A068228.

Sequence in context: A350845 A315723 A361908 * A315724 A146538 A154373

Adjacent sequences: A160591 A160592 A160593 * A160595 A160596 A160597

Keyword

nonn

Author

M. F. Hasler, May 22 2009

Status

approved