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.

A190352 The continued fraction expansion of tanh(Pi) requires the computation of the pairs (p_n, q_n); sequence gives values of q_n.

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%I A190352 #14 Feb 12 2019 23:27:04
%S A190352 1,1,268,1073,15290,16363,48016,64379,176774,417927,594701,1607329,
%T A190352 5416688,44940833,140239187,185180020,1066139287,4449737168,
%U A190352 5515876455,81672007538,822235951835,903907959373,18900395139295,719118923252583,738019318391878
%N A190352 The continued fraction expansion of tanh(Pi) requires the computation of the pairs (p_n, q_n); sequence gives values of q_n.
%C A190352 a(2) = 268 explains the comment in A021085 that "The decimal expansion of Sum_{n>=1} floor(n * tanh(Pi))/10^n is the same as that of 1/81 for the first 268 decimal places [Borwein et al.]".
%D A190352 J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 13.
%H A190352 G. C. Greubel, <a href="/A190352/b190352.txt">Table of n, a(n) for n = 0..1920</a>
%F A190352 a(n) = A060402(n)*a(n-1) + a(n-2) for n >= 2. - _Nathaniel Johnston_, May 10 2011
%p A190352 lim:=50: with(numtheory): cfr := cfrac(tanh(Pi),lim+10,'quotients'): q[0]:=1:q[1]:=cfr[2]: printf("%d, %d, ", q[0], q[1]): for n from 2 to lim do q[n]:=cfr[n+1]*q[n-1]+q[n-2]: printf("%d, ",q[n]): od: # _Nathaniel Johnston_, May 10 2011
%t A190352 a[0] := 1; a[1] := 1; A060402:= ContinuedFraction[Tanh[Pi], 100];
%t A190352 a[n_]:= a[n] = A060402[[n + 1]]*a[n - 1] + a[n - 2]; Join[{1, 1}, Table[a[n], {n, 2, 75}]] (* _G. C. Greubel_, Apr 05 2018 *)
%Y A190352 Cf. A060402, A021085.
%K A190352 nonn
%O A190352 0,3
%A A190352 _N. J. A. Sloane_, May 09 2011
%E A190352 a(4)-a(24) from _Nathaniel Johnston_, May 10 2011