A073740 Self-convolution of A073739; odd-indexed terms are twice the odd primes.

1, 2, 3, 6, 5, 10, 10, 14, 20, 22, 39, 26, 64, 34, 104, 38, 152, 46, 225, 58, 308, 62, 434, 74, 556, 82, 763, 86, 936, 94, 1224, 106, 1488, 118, 1857, 122, 2244, 134, 2706, 142, 3232, 146, 3827, 158, 4472, 166, 5240, 178, 6020, 194, 6997, 202, 7936, 206, 9122

Offset: 0

Author

Paul D. Hanna, Aug 07 2002

Keywords

• easy
• nice
• nonn
• look

Comments

The first odd prime is here considered to be p_0 = 1.

Examples

			a(9) = 2*p_4 = 22; a(8) = 1*0+1*4+1*0+2*3+0*0+3*2+0*1+4*1+0*1 = 20.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A036467, A073739.

Programs

Haskell

a073740 n = a073740_list !! n
a073740_list = tail $ f a073739_list [] where
   f (x:xs) ys = (sum $ zipWith (*) ys a073739_list) : f xs (x : ys)
-- Reinhard Zumkeller, Aug 09 2015

Mathematica

(* b = A073739 *) b[n_ /; n <= 2] = 1; b[?EvenQ] = 0; b[n] := b[n] = Prime[(n+1)/2] - b[n-2]; a[0] = 1; a[1] = 2; a[n_?OddQ] := 2*Prime[(n-1)/2+1]; a[n_?EvenQ] := Sum[b[k]*b[n-k], {k, 0, n}]; Table[a[n], {n, 0, 54}] (* Jean-François Alcover, Aug 01 2013 *)

Formula

a(0) = 1, a(2n+1) = 2*p_n, a(2n) = Sum_{k=0..2n} A073739(k)*A073739(2n-k).