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%I #24 May 19 2021 16:04:32
%S 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,
%T 36,37,38,43,44,46,47,50,51,53,55,56,58,60,61,64,65,66,67,71,75,76,77,
%U 78,80,81,84,86,88,90,91,93,94,95,98,103,104,105,106,111,113,116,117,118
%N Indices of primes in A007310.
%C 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.
%C Indices 1 and 9 (1 and 25) are the smallest nonprimes.
%H Grant Garcia, <a href="/A181709/b181709.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) = floor(prime(n+2)/3)+1 = A144769(n+2)+1. - _Gary Detlefs_, Dec 11 2011
%F a(n) ~ n*log(n)/3. - _Ilya Gutkovskiy_, Jul 18 2016
%e A007310(2), 5, is the first prime of the sequence.
%e A007310(50), 149, is also a prime, hence 50 is included.
%t Floor[Prime[Range[3,80]]/3]+1 (* _Harvey P. Dale_, Sep 12 2019 *)
%o (Python)
%o from sympy import isprime
%o out = ""
%o for n,p in enumerate(isprime((6*n+(-1)**n-3)//2) for n in range(1,1000)):
%o out+=["","%s "%str(n+1)][p]
%o for n,p in enumerate(out.rstrip(" ").split(" ")): print(n+1,p)
%Y Cf. A007310, A000040.
%K easy,nonn
%O 1,1
%A _Grant Garcia_, Nov 07 2010
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