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A181709
Indices of primes in A007310.
3
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
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
Sequence in context: A076487 A317717 A356841 * A320058 A320057 A374129
KEYWORD
easy,nonn
AUTHOR
Grant Garcia, Nov 07 2010
STATUS
approved