A091177 Numbers m such that the m-th prime is of the form 3*k-1.

1, 3, 5, 7, 9, 10, 13, 15, 16, 17, 20, 23, 24, 26, 28, 30, 32, 33, 35, 39, 40, 41, 43, 45, 49, 51, 52, 54, 55, 56, 57, 60, 62, 64, 66, 69, 71, 72, 76, 77, 79, 81, 83, 86, 87, 89, 91, 92, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 113, 116, 118, 119, 120, 123

Offset: 1

Author

Ray Chandler, Dec 26 2003

Keywords

• nonn
• easy

Comments

A003627 indexed by A000040.

The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - Amiram Eldar, Feb 28 2021

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003627 (primes of the form 3*k-1), A024893, A087370, A088879.

A133677 is another version.

Programs

Mathematica

PrimePi/@Select[3Range[0,250]-1,PrimeQ]  (* Harvey P. Dale, Apr 26 2011 *)
Select[Range[150],IntegerQ[(Prime[#]+1)/3]&] (* Harvey P. Dale, Dec 14 2021 *)

PARI

a091177(limit)={my(m=0);forprime(p=2,prime(limit),m++;if(p%3==2,print1(m,", ")))};
a091177(123) \\ Hugo Pfoertner, Aug 03 2021

Formula

a(n) = k such that A000040(k) = A003627(n).