OFFSET
0,5
COMMENTS
If any term of even index greater than 2 is equal to 0 then the Goldbach conjecture would be disproved.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{k=1..n-1} P(k)*P(n-k) where P(k) = A061397(k).
MAPLE
a:= n-> (f-> add(f(j)*f(n-j), j=0..n))(k-> `if`(isprime(k), k, 0)):
seq(a(n), n=0..60); # Alois P. Heinz, May 11 2020
MATHEMATICA
Table[Sum[If[PrimeQ[k], k, 0]*If[PrimeQ[n-k], n-k, 0], {k, 0, n}], {n, 0, 100}] (* Vaclav Kotesovec, May 10 2020 *)
PROG
(Python)
def a(n):
A061397 = [0]+[factorial(2*i-1)%(i**2) for i in range(1, n+1)]
sum = 0
for i in range(1, n):
return sum
(PARI) P(n) = if (isprime(n), n);
a(n) = sum(k=1, n-1, P(k)*P(n-k)); \\ Michel Marcus, May 10 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lawrence Pepper, May 10 2020
STATUS
approved