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A285407 G.f.: 1/(1 - x^2/(1 - x^3/(1 - x^5/(1 - x^7/(1 - x^11/(1 - ... - x^prime(k)/(1 - ... ))))))), a continued fraction. 5
1, 0, 1, 0, 1, 1, 1, 2, 2, 3, 5, 5, 9, 11, 15, 23, 28, 43, 57, 78, 113, 149, 214, 293, 403, 569, 774, 1086, 1502, 2072, 2896, 3986, 5548, 7691, 10636, 14797, 20459, 28400, 39386, 54542, 75724, 104886, 145468, 201733, 279545, 387786, 537472, 745233, 1033383, 1432415, 1986394 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Robert Israel, Table of n, a(n) for n = 0..5000

FORMULA

a(n) ~ c * d^n, where d = 1.3864622092472465020397266918102624708859968795203700659786636158522760956... and c = 0.15945087310540003725148530084775272562567007586487061850065597143186... - Vaclav Kotesovec, Aug 25 2017

EXAMPLE

G.f.: A(x) = 1 + x^2 + x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + 3*x^9 + 5*x^10 + ...

MAPLE

R:= 1:

for i from numtheory:-pi(50) to 1 by -1 do

  R:= series(1-x^ithprime(i)/R, x, 51);

od:

R:= series(1/R, x, 51):

seq(coeff(R, x, j), j=0..50); # Robert Israel, Apr 20 2017

MATHEMATICA

nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^Prime[k], 1, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000040, A206739, A206741, A206742, A206743, A227310, A269353.

Sequence in context: A060048 A110699 A035537 * A292802 A247376 A101779

Adjacent sequences:  A285404 A285405 A285406 * A285408 A285409 A285410

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 18 2017

STATUS

approved

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Last modified October 26 21:33 EDT 2021. Contains 348269 sequences. (Running on oeis4.)