%I #4 Jan 22 2017 21:53:08

%S 1,0,0,1,0,1,1,0,2,1,1,4,1,3,6,2,8,9,5,16,13,14,30,20,33,51,37,72,84,

%T 76,142,141,164,264,247,344,473,462,694,836,903,1344,1494,1799,2520,

%U 2734,3566,4638,5145,6951,8489,9875,13295,15632,19110,25037,29130,36919,46732,54969,70798,87026,104653,134585,162550

%N Expansion of 1/(1 - Sum_{k>=1} x^prime(prime(k))).

%C Number of compositions (ordered partitions) of n into primes with prime subscripts (A006450).

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

%F G.f.: 1/(1 - Sum_{k>=1} x^prime(prime(k))).

%e a(11) = 4 because we have [11], [5, 3, 3], [3, 5, 3] and [3, 3, 5], where 3 = prime(2) = prime(prime(1)), 5 = prime(3) = prime(prime(2)) and 11 = prime(5) = prime(prime(3)).

%t nmax = 64; CoefficientList[Series[1/(1 - Sum[x^Prime[Prime[k]], {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A006450, A023360, A271368, A278912, A280917.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Jan 21 2017