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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
OFFSET
0,3
COMMENTS
Partial sums of A023360.
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 28 2018
STATUS
approved