

A237768


Number of primes p < n with pi(np) a Sophie Germain prime, where pi(.) is given by A000720.


7



0, 0, 0, 0, 1, 2, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 5, 5, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 1, 1, 3, 3, 5, 5, 2, 2, 1, 1, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 1
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OFFSET

1,6


COMMENTS

Conjecture: a(n) > 0 for all n > 4, and a(n) = 1 only for n = 5, 12, 20, 21, 26, 27, 30, 31, 32, 60, 61, 68, 69, 80, 81.
This is stronger than part (i) of the conjecture in A237705.
We have verified that a(n) > 0 for all n = 5, ..., 2*10^7.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000


EXAMPLE

a(5) = 1 since 2, pi(52) = pi(3) = 2 and 2*2 + 1 = 5 are all prime.
a(12) = 1 since 7, pi(127) = pi(5) = 3 and 2*3 + 1 = 7 are all prime.
a(81) = 1 since 47, pi(8147) = pi(34) = 11 and 2*11 + 1 = 23 are all prime.


MATHEMATICA

sg[n_]:=PrimeQ[n]&&PrimeQ[2n+1]
a[n_]:=Sum[If[sg[PrimePi[nPrime[k]]], 1, 0], {k, 1, PrimePi[n1]}]
Table[a[n], {n, 1, 80}]


CROSSREFS

Cf. A000040, A000720, A005384, A237284, A237705, A237706.
Sequence in context: A237721 A254296 A248371 * A237705 A340673 A031284
Adjacent sequences: A237765 A237766 A237767 * A237769 A237770 A237771


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 13 2014


STATUS

approved



