A237819 Number of primes p < n such that floor(sqrt(n-p)) is a Sophie Germain prime.

0, 0, 0, 0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 6, 6, 6, 7, 6, 7, 7, 7, 6, 7, 6, 6, 7, 7, 5, 6, 5, 6, 6, 6, 4, 4, 4, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 7, 6, 6, 6, 6, 5, 6, 5, 5

Offset

1,7

Comments

Conjecture: (i) a(n) > 0 for all n > 5.

(ii) For any integer n > 10, there is a prime p < n such that q = floor(sqrt(n-p)) and q + 2 are both prime.

Links

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

Example

a(6) = 1 since 2, floor(sqrt(6-2)) = 2 and 2*2 + 1 = 5 are all prime.

Mathematica

f[n_]:=Floor[Sqrt[n]]
q[n_]:=PrimeQ[f[n]]&&PrimeQ[2*f[n]+1]
a[n_]:=Sum[If[q[n-Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}]
Table[a[n], {n, 1, 80}]

Crossrefs

Cf. A000040, A001359, A005384, A006512, A237720, A237721, A237815, A237817.

Sequence in context: A123087 A071868 A179390 * A082447 A139789 A366033

Adjacent sequences: A237816 A237817 A237818 * A237820 A237821 A237822

Keyword

nonn

Author

Zhi-Wei Sun, Feb 13 2014

Status

approved