|
%I #10 Mar 17 2017 09:31:47
%S 5,12,44,51,280,949,103488,133416,4142957,81015132,141119360,
%T 2339121011,22104171804,658972588452,461228244281,3140753982224,
%U 7467448353120,49702513350325,3912991025369532,130254818350668557,177768662787348689760
%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to e.
%C See A195500 for a discussion and references.
%t r = E; z = 23;
%t p[{f_, n_}] := (#1[[2]]/#1[[
%t 1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t 2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t Array[FromContinuedFraction[
%t ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t p[{r, z}]] (* A195541, A195542 *)
%t Sqrt[a^2 + b^2] (* A195543 *)
%t (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y Cf. A195500, A195542, A195543.
%K nonn
%O 1,1
%A _Clark Kimberling_, Sep 20 2011
| 