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%I A281422 #4 Jan 22 2017 21:53:08
%S A281422 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 A281422 76,142,141,164,264,247,344,473,462,694,836,903,1344,1494,1799,2520,
%U A281422 2734,3566,4638,5145,6951,8489,9875,13295,15632,19110,25037,29130,36919,46732,54969,70798,87026,104653,134585,162550
%N A281422 Expansion of 1/(1 - Sum_{k>=1} x^prime(prime(k))).
%C A281422 Number of compositions (ordered partitions) of n into primes with prime subscripts (A006450).
%H A281422 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A281422 G.f.: 1/(1 - Sum_{k>=1} x^prime(prime(k))).
%e A281422 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 A281422 nmax = 64; CoefficientList[Series[1/(1 - Sum[x^Prime[Prime[k]], {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A281422 Cf. A006450, A023360, A271368, A278912, A280917.
%K A281422 nonn
%O A281422 0,9
%A A281422 _Ilya Gutkovskiy_, Jan 21 2017

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