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.

A163168 Pierce expansion of sech(1).

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%I A163168 #6 Feb 16 2025 08:33:11
%S A163168 1,2,3,8,9,24,37,85,1115,29153,423233,2208087,5102497,9813637,
%T A163168 15922076,19204759,106559540,120015709,1493877142,2199074984,
%U A163168 32818755269,1505298832166,1507229768977,2841536357911,14805574584765
%N A163168 Pierce expansion of sech(1).
%C A163168 Pierce expansion of A073746.
%H A163168 G. C. Greubel, <a href="/A163168/b163168.txt">Table of n, a(n) for n = 1..1000</a>
%H A163168 Eric Weisstein, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>, Mathworld.
%F A163168 0.648054... = 1/1 - 1/(1*2) + 1/(1*2*3) - 1/(1*2*3*8) + 1/(1*2*3*8*9) - ...
%t A163168 PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[Sech[1] , 7!], 50] (* _G. C. Greubel_, Nov 14 2016 *)
%K A163168 nonn
%O A163168 1,2
%A A163168 _R. J. Mathar_, Jul 22 2009