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

0,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A036467, A073739.

Sequence in context: A055944 A331633 A350801 * A239956 A077320 A339195

Adjacent sequences: A073737 A073738 A073739 * A073741 A073742 A073743

Keyword

easy,nice,nonn,look

Author

Paul D. Hanna, Aug 07 2002

Status

approved