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A237768 Number of primes p < n with pi(n-p) 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 (list; graph; refs; listen; history; text; internal format)
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

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5) = 1 since 2, pi(5-2) = pi(3) = 2 and 2*2 + 1 = 5 are all prime.

a(12) = 1 since 7, pi(12-7) = pi(5) = 3 and 2*3 + 1 = 7 are all prime.

a(81) = 1 since 47, pi(81-47) = 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[n-Prime[k]]], 1, 0], {k, 1, PrimePi[n-1]}]

Table[a[n], {n, 1, 80}]

CROSSREFS

Cf. A000040, A000720, A005384, A237284, A237705, A237706.

Sequence in context: A237721 A254296 A248371 * A237705 A031284 A064569

Adjacent sequences:  A237765 A237766 A237767 * A237769 A237770 A237771

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 13 2014

STATUS

approved

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Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)