A091177 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

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

A133677 is another version.

Sequence in context: A348017 A187347 A187413 * A066929 A173909 A165249

Adjacent sequences: A091174 A091175 A091176 * A091178 A091179 A091180

KEYWORD

nonn,easy

AUTHOR

Ray Chandler, Dec 26 2003

STATUS

approved