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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.
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%I #13 Aug 25 2017 03:25:51

%S 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,

%T 569,774,1086,1502,2072,2896,3986,5548,7691,10636,14797,20459,28400,

%U 39386,54542,75724,104886,145468,201733,279545,387786,537472,745233,1033383,1432415,1986394

%N 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.

%H Robert Israel, <a href="/A285407/b285407.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ c * d^n, where d = 1.3864622092472465020397266918102624708859968795203700659786636158522760956... and c = 0.15945087310540003725148530084775272562567007586487061850065597143186... - _Vaclav Kotesovec_, Aug 25 2017

%e 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 + ...

%p R:= 1:

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

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

%p od:

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

%p seq(coeff(R,x,j),j=0..50); # _Robert Israel_, Apr 20 2017

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

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

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Apr 18 2017