cp's OEIS Frontend

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

%I A073740 #17 Mar 15 2023 14:37:12
%S A073740 1,2,3,6,5,10,10,14,20,22,39,26,64,34,104,38,152,46,225,58,308,62,434,
%T A073740 74,556,82,763,86,936,94,1224,106,1488,118,1857,122,2244,134,2706,142,
%U A073740 3232,146,3827,158,4472,166,5240,178,6020,194,6997,202,7936,206,9122
%N A073740 Self-convolution of A073739; odd-indexed terms are twice the odd primes.
%C A073740 The first odd prime is here considered to be p_0 = 1.
%H A073740 Reinhard Zumkeller, <a href="/A073740/b073740.txt">Table of n, a(n) for n = 0..10000</a>
%F A073740 a(0) = 1, a(2n+1) = 2*p_n, a(2n) = Sum_{k=0..2n} A073739(k)*A073739(2n-k).
%e A073740 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.
%t A073740 (* 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 *)
%o A073740 (Haskell)
%o A073740 a073740 n = a073740_list !! n
%o A073740 a073740_list = tail $ f a073739_list [] where
%o A073740    f (x:xs) ys = (sum $ zipWith (*) ys a073739_list) : f xs (x : ys)
%o A073740 -- _Reinhard Zumkeller_, Aug 09 2015
%Y A073740 Cf. A036467, A073739.
%K A073740 easy,nice,nonn,look
%O A073740 0,2
%A A073740 _Paul D. Hanna_, Aug 07 2002