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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 01 2014
STATUS
approved