A073739 - OEIS

%I #16 Dec 27 2018 00:39:33

%S 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,

%T 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,

%U 55,0,58,0,69,0,62,0,75,0,64,0,85,0,66

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

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

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

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

%t 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 *)

%o (Haskell)

%o import Data.List (transpose)

%o a073739 n = a073739_list !! n

%o a073739_list = concat $ transpose [1 : 1 : repeat 0, tail a036467_list]

%o -- _Reinhard Zumkeller_, Aug 09 2015

%Y Cf. A036467, A073740.

%K easy,nice,nonn

%O 0,4

%A _Paul D. Hanna_, Aug 07 2002