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

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, 201, 277, 341, 438, 575, 707, 947, 1169, 1530, 1949, 2474, 3228, 4046, 5281, 6678, 8594, 11035, 14025, 18142, 23015, 29681, 37888, 48512, 62319, 79456, 102230, 130456, 167418, 214356, 274221, 351904, 449700, 577024, 738150

Offset

0,8

Comments

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

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

Links

Table of n, a(n) for n=0..60.

Eric Weisstein's World of Mathematics, Prime Sums

Index entries for sequences related to compositions

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A318611 A366472 A130067 * A032303 A032215 A117363

Adjacent sequences: A282903 A282904 A282905 * A282907 A282908 A282909

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2017

Status

approved