A265835 Numbers n such that A015128(n)/2 is prime.

2, 4, 16, 36, 400, 1296, 1521, 52441

Offset: 1

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

• nonn
• more
• hard

Comments

Next term, if it exists, is greater than 4000000. - Vaclav Kotesovec, updated Apr 12 2017

The values of a(n) are the squares of these integers for 1 < n < 9: 2, 4, 6, 20, 36, 39, 229. Squares also appear in the sequence of numbers k such that A015128(k)/2 is semiprime. - Altug Alkan, Dec 16 2015

Examples

			4 is a term because A015128(4)/2 = 14/2 = 7 is prime.
		

Crossrefs

Cf. A014968, A015128, A035359, A046063, A299961.

Programs

Mathematica

Select[Range[2000], PrimeQ[Sum[PartitionsP[#-k]*PartitionsQ[k], {k, 0, #}]/2] &]

PARI

a015128(n) = polcoeff(exp(sum(m=1, n\2+1, 2*x^(2*m-1)/(1-x^(2*m-1)+x*O(x^n))/(2*m-1))), n);
for(n=1, 1e3, if(ispseudoprime(a015128(n)/2), print1(n, ", "))) \\ Altug Alkan, Dec 16 2015