A181709 Indices of primes in A007310.

2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 20, 21, 23, 24, 25, 27, 28, 30, 33, 34, 35, 36, 37, 38, 43, 44, 46, 47, 50, 51, 53, 55, 56, 58, 60, 61, 64, 65, 66, 67, 71, 75, 76, 77, 78, 80, 81, 84, 86, 88, 90, 91, 93, 94, 95, 98, 103, 104, 105, 106, 111, 113, 116, 117, 118

Offset

1,1

Comments

All primes but 2 and 3 are present in A007310, making this sequence an efficient method for storing large quantities of primes. To unpack this sequence into primes, use the formula (6n + (-1)^n - 3) / 2.

Indices 1 and 9 (1 and 25) are the smallest nonprimes.

Links

Grant Garcia, Table of n, a(n) for n=1..10000

Formula

a(n) = floor(prime(n+2)/3)+1 = A144769(n+2)+1. - Gary Detlefs, Dec 11 2011

a(n) ~ n*log(n)/3. - Ilya Gutkovskiy, Jul 18 2016

Example

A007310(2), 5, is the first prime of the sequence.
A007310(50), 149, is also a prime, hence 50 is included.

Mathematica

Floor[Prime[Range[3, 80]]/3]+1 (* Harvey P. Dale, Sep 12 2019 *)

Prog

(Python)
from sympy import isprime
out = ""
for n, p in enumerate(isprime((6*n+(-1)**n-3)//2) for n in range(1, 1000)):
    out+=["", "%s "%str(n+1)][p]
for n, p in enumerate(out.rstrip(" ").split(" ")): print(n+1, p)

Crossrefs

Cf. A007310, A000040.

Sequence in context: A076487 A317717 A356841 * A320058 A320057 A374129

Adjacent sequences: A181706 A181707 A181708 * A181710 A181711 A181712

Keyword

easy,nonn

Author

Grant Garcia, Nov 07 2010

Status

approved