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A303665 Expansion of 1/((1 - x)*(1 - Sum_{k>=1} x^prime(k))). 0
1, 1, 2, 3, 4, 7, 9, 15, 21, 31, 47, 67, 102, 148, 220, 325, 477, 709, 1041, 1542, 2274, 3355, 4959, 7311, 10804, 15940, 23535, 34747, 51281, 75723, 111762, 165005, 243578, 359567, 530831, 783585, 1156799, 1707662, 2520913, 3721467, 5493674, 8110012, 11972133, 17673686 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A023360.

LINKS

Table of n, a(n) for n=0..43.

Index entries for sequences related to compositions

MAPLE

b:= proc(n) option remember; `if`(n=0, 1,

      add(`if`(isprime(j), b(n-j), 0), j=2..n))

    end:

a:= proc(n) option remember;

      `if`(n<0, 0, b(n)+a(n-1))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 28 2018

MATHEMATICA

nmax = 43; CoefficientList[Series[1/((1 - x) (1 - Sum[x^Prime[k], {k, 1, nmax}])), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[Boole[PrimeQ[k]] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 43}]]

CROSSREFS

Cf. A000040, A010051, A023360, A034891.

Sequence in context: A321535 A108809 A276846 * A027947 A324736 A293853

Adjacent sequences:  A303662 A303663 A303664 * A303666 A303667 A303668

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 28 2018

STATUS

approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)