%I #6 Jan 22 2017 21:53:15

%S 0,0,0,1,2,1,0,2,2,0,2,3,0,0,2,0,0,3,2,0,0,2,2,2,2,0,2,0,0,2,0,3,2,0,

%T 0,4,4,0,2,2,0,1,2,2,2,2,0,2,0,2,4,0,0,0,2,0,2,4,0,1,2,0,2,4,0,2,2,1,

%U 0,2,2,2,2,0,0,4,0,0,0,2,2,2,0,1,6,0,0,2,2,0,0,2,2,2,2,2,2,4,4,2,0,2,0,0,2,4,0,2,4,1,2,4

%N Expansion of (Sum_{k>=1} x^prime(prime(k)))^2 [even terms only].

%C Number of ways to write 2n as an ordered sum of two primes with prime subscripts (A006450).

%H Ilya Gutkovskiy, <a href="/A281423/a281423.pdf">Extended graphical example</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: (Sum_{k>=1} x^prime(prime(k)))^2 [even terms only].

%e a(4) = 2 because we have [3, 5] and [5, 3], where 3 = prime(2) = prime(prime(1)) and 5 = prime(3) = prime(prime(2)).

%t Take[CoefficientList[Series[Sum[x^Prime[Prime[k]], {k, 1, 250}]^2, {x, 0, 250}], x], {1, -1, 2}]

%Y Cf. A001031, A002375, A006450, A045917, A073610, A281422.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Jan 21 2017