

A181709


Indices of primes in A007310.


2



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
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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) import pyecm
# pyecm can be obtained from pyecm.sourceforge.net
out = ""
for n, p in enumerate([pyecm.isprime((6*n+(1)**n3)/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: A039218 A076487 A317717 * A320058 A320057 A033106
Adjacent sequences: A181706 A181707 A181708 * A181710 A181711 A181712


KEYWORD

easy,nonn


AUTHOR

Grant Garcia, Nov 07 2010


STATUS

approved



