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A282906 Expansion of 1/(1 - Sum_{j>=1} x^(Sum_{i=1..j} prime(i))). 1

%I

%S 1,0,1,0,1,1,1,2,1,3,3,4,6,5,10,9,15,18,21,32,33,52,58,79,102,122,172,

%T 201,277,341,438,575,707,947,1169,1530,1949,2474,3228,4046,5281,6678,

%U 8594,11035,14025,18142,23015,29681,37888,48512,62319,79456,102230,130456,167418,214356,274221,351904,449700,577024,738150

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

%C Number of compositions (ordered partitions) of n into partial sums of primes (A007504).

%C Conjecture: every number > 3 is the sum of at most 5 partial sums of primes.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>

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

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

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

%t nmax = 60; CoefficientList[Series[1/(1 - Sum[x^Sum[Prime[i], {i, 1, j}], {j, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A007504, A023360, A084143, A281273, A281274.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Feb 24 2017

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Last modified October 21 19:27 EDT 2018. Contains 316428 sequences. (Running on oeis4.)