A272428 - OEIS

A272428

Expansion of the continued fraction x/(1-pi(2)*x/(1-pi(3)*x/(1-pi(4)*x/(1-...)))).

0, 1, 1, 3, 13, 71, 461, 3447, 29093, 272767, 2797069, 30897015, 362691733, 4475707535, 57612706973, 769779683367, 10648337804645, 152377871778559, 2256813406989421, 34636615303780503

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OFFSET

0,4

COMMENTS

The initial similarity with A233824 may explain that method's success in representing pi(n).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

FORMULA

G.f.: x/(1-pi(2)*x/(1-pi(3)*x/(1-pi(4)*x/(1-...)))) a continued fraction.

MATHEMATICA

CoefficientList[Series[x/(1 + ContinuedFractionK[-x*PrimePi[k], 1, {k, 2, 60}]), {x, 0, 60}], x]

CROSSREFS

Cf. A000720, A233824.

Sequence in context: A162326 A122455 A126390 * A167894 A158882 A233824

Adjacent sequences: A272425 A272426 A272427 * A272429 A272430 A272431

KEYWORD

nonn

AUTHOR

Benedict W. J. Irwin, Apr 29 2016

STATUS

approved