A073739 Least positive integers whose convolution forms a sequence whose odd-indexed terms are twice the odd primes (see: A073740).

1, 1, 1, 2, 0, 3, 0, 4, 0, 7, 0, 6, 0, 11, 0, 8, 0, 15, 0, 14, 0, 17, 0, 20, 0, 21, 0, 22, 0, 25, 0, 28, 0, 31, 0, 30, 0, 37, 0, 34, 0, 39, 0, 40, 0, 43, 0, 46, 0, 51, 0, 50, 0, 53, 0, 54, 0, 55, 0, 58, 0, 69, 0, 62, 0, 75, 0, 64, 0, 85, 0, 66

Offset: 0

Author

Paul D. Hanna, Aug 07 2002

Keywords

• easy
• nice
• nonn

Comments

The odd-indexed bisection forms A036467, in which the pairwise sums yield the primes.

Examples

			a(10) = p_10 +p_8 +p_6 +p_4 +p_2 +p_0 = 29 + 19 + 13 +7 +3 + 1 = 72.
		

Crossrefs

Cf. A036467, A073740.

Programs

Haskell

import Data.List (transpose)
a073739 n = a073739_list !! n
a073739_list = concat $ transpose [1 : 1 : repeat 0, tail a036467_list]
-- Reinhard Zumkeller, Aug 09 2015

Mathematica

a[n_ /; n <= 2] = 1; a[?EvenQ] = 0; a[n] := a[n] = Prime[(n + 1)/2] - a[n - 2]; Table[a[n], {n, 0, 71}] (* Jean-François Alcover, Aug 01 2013 *)

Formula

a(n) = p_n - p_{n-1} when n>1, where a(0)=a(1)=1.