The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A303665

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A303665

Expansion of 1/((1 - x)*(1 - Sum_{k>=1} x^prime(k))).
(history; published version)

#6 by Bruno Berselli at Sat Apr 28 17:13:59 EDT 2018

STATUS

proposed

approved

#5 by Alois P. Heinz at Sat Apr 28 16:46:54 EDT 2018

STATUS

editing

proposed

#4 by Alois P. Heinz at Sat Apr 28 16:46:51 EDT 2018

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

STATUS

proposed

editing

#3 by Ilya Gutkovskiy at Sat Apr 28 12:25:26 EDT 2018

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Sat Apr 28 04:20:22 EDT 2018

NAME

allocated for Ilya Gutkovskiy

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

DATA

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.

LINKS

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

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.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Apr 28 2018

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Apr 28 04:20:22 EDT 2018

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved