OFFSET
1,11
COMMENTS
Conjecture: For any integer n > 0, we have a(n+r) > 0 for some r = 0,1,2,3,4,5. Moreover, if n = 6*k + 2, then a(n) > 0 except for k = 0, 1, 12, 28, 102, 117, 168, 4079.
We have verified the conjecture for n up to 10^9.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: (Sum_{k>=1} x^prime(k))*(Sum_{k>=1} x^(prime(k)^2)). - Ilya Gutkovskiy, Feb 05 2017
EXAMPLE
a(11) = 2 since 11 = 2^2 + 7 = 3^2 + 2 with 2, 3, 7 all prime.
MATHEMATICA
Do[r=0; Do[If[PrimeQ[n-Prime[k]^2], r=r+1], {k, 1, PrimePi[Sqrt[n]]}]; Print[n, " ", r]; Continue, {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 22 2015
STATUS
approved