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A182663 Number of ordered ways to write n = p + q with q > 0 such that p and 2*p + prime(q) are both prime. 1
0, 0, 0, 1, 0, 2, 2, 2, 3, 3, 1, 1, 1, 3, 3, 5, 2, 2, 4, 1, 4, 4, 4, 3, 1, 3, 3, 3, 7, 4, 4, 2, 3, 1, 3, 5, 2, 2, 5, 6, 1, 6, 5, 2, 4, 6, 4, 3, 3, 4, 4, 6, 4, 3, 5, 2, 3, 5, 5, 2, 6, 3, 6, 5, 5, 4, 7, 4, 4, 8, 6, 6, 5, 5, 4, 8, 7, 6, 4, 4, 5, 6, 4, 5, 4, 3, 7, 9, 9, 4, 8, 5, 6, 2, 9, 6, 7, 1, 7, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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

(ii) Any integer n > 5 can be written as p + q (q > 0) with p and prime(p) + 2*q both prime.

(iii) Each integer n > 10 can be written as p + q (q > 0) with p and prime(p)^2 + 4*q^2 both prime.

LINKS

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

EXAMPLE

a(11) = 1 since 11 = 5 + 6 with 5 and 2*5 + prime(6) = 10 + 13 = 23 both prime.

a(98) = 1 since 98 = 19 + 79 with 19 and 2*19 + prime(79) = 38 + 401 = 439 both prime.

MATHEMATICA

p[n_, m_]:=PrimeQ[2*m+Prime[n-m]]

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

Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000040, A182662, A236831.

Sequence in context: A125600 A084053 A331553 * A071452 A282495 A341421

Adjacent sequences:  A182660 A182661 A182662 * A182664 A182665 A182666

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 01 2014

STATUS

approved

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Last modified April 12 11:30 EDT 2021. Contains 342920 sequences. (Running on oeis4.)