cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A225436 Denominators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).

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%I A225436 #40 Jun 02 2025 08:34:12
%S A225436 1,3,3,9,12,39,123,87,771,1473,11427,46779,19533,212559,1890093,
%T A225436 8691981,1570137,9863961,486463449,2459255649,6337494039,16694653089,
%U A225436 7166066763,51605000913,2729643372111,7738039298811,89176449644619,104501330075607,1554311845035993,361227369257943
%N A225436 Denominators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).
%C A225436 1
%H A225436 Seiichi Manyama, <a href="/A225436/b225436.txt">Table of n, a(n) for n = 1..843</a>
%H A225436 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFractionConstants.html">Continued Fraction Constants</a>
%H A225436 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedContinuedFraction.html">Generalized Continued Fraction</a>
%F A225436 E.g.f: (1/2)*(2+e^((1/2)*(1+z)^2)*sqrt(2*Pi)*(1+z)*(-erf(1/sqrt(2))+erf((1+z)/sqrt(2)))).
%F A225436 Limit_{n->oo} A225435(n)/a(n) = sqrt(2/(e*Pi))/erfc(1/sqrt(2))-1 = A111129.
%e A225436 1, 1/3, 2/3, 4/9, 7/12, 19/39, ... = A225435(n)/A225436(n).
%t A225436 Denominator[Table[ContinuedFractionK[k, 1, {k, 1, n}], {n, 30}]]
%Y A225436 Cf. A225435 (numerators).
%Y A225436 Cf. A111129 (decimal digits of infinite c.f.).
%Y A225436 Related to A000932.
%K A225436 nonn,frac
%O A225436 1,2
%A A225436 _Eric W. Weisstein_, May 07 2013