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A237837 Number of primes p < n such that the number of Sophie Germain primes among 1, ..., n-p is a cube. 1
0, 0, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 3, 3, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Conjecture: a(n) > 0 for all n > 53.

LINKS

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

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

EXAMPLE

a(55) = 2 since 53 is prime and there is exactly 1^3 = 1 Sophie Germain prime not exceeding 55 - 53 = 2, and 2 is prime and there are exactly 2^3 = 8 Sophie Germain primes not exceeding 55 - 2 = 53 (namely, they are 2, 3, 5, 11, 23, 29, 41, 53).

MATHEMATICA

sg[n_]:=Sum[If[PrimeQ[2*Prime[k]+1], 1, 0], {k, 1, PrimePi[n]}]

CQ[n_]:=IntegerQ[n^(1/3)]

a[n_]:=Sum[If[CQ[sg[n-Prime[k]]], 1, 0], {k, 1, PrimePi[n-1]}]

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

CROSSREFS

Cf. A000040, A000578, A005384, A237815.

Sequence in context: A321761 A037819 A090405 * A168509 A079635 A037909

Adjacent sequences:  A237834 A237835 A237836 * A237838 A237839 A237840

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 13 2014

STATUS

approved

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Last modified December 1 09:39 EST 2021. Contains 349426 sequences. (Running on oeis4.)