A278912 -id:A278912

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A281422

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

+0
1

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, 76, 142, 141, 164, 264, 247, 344, 473, 462, 694, 836, 903, 1344, 1494, 1799, 2520, 2734, 3566, 4638, 5145, 6951, 8489, 9875, 13295, 15632, 19110, 25037, 29130, 36919, 46732, 54969, 70798, 87026, 104653, 134585, 162550

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OFFSET

0,9

COMMENTS

Number of compositions (ordered partitions) of n into primes with prime subscripts (A006450).

LINKS

Table of n, a(n) for n=0..64.

Index entries for sequences related to compositions

FORMULA

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

EXAMPLE

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)).

MATHEMATICA

nmax = 64; CoefficientList[Series[1/(1 - Sum[x^Prime[Prime[k]], {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A006450, A023360, A271368, A278912, A280917.

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 21 2017

STATUS

approved

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