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A073740
Self-convolution of A073739; odd-indexed terms are twice the odd primes.
2
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
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
Sequence in context: A055944 A331633 A350801 * A239956 A077320 A339195
KEYWORD
easy,nice,nonn,look
AUTHOR
Paul D. Hanna, Aug 07 2002
STATUS
approved