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

Author

Grant Garcia, Nov 07 2010

Keywords

• easy
• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A007310, A000040.

Programs

Mathematica

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

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)

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