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.

A059186 Engel expansion of Pi^2/6, or zeta(2) = 1.64493.

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%I A059186 #30 Apr 13 2018 11:20:22
%S A059186 1,2,4,7,9,22,35,79,2992,3597,17523,28632,41470,53093,57406,14504930,
%T A059186 42622213,188335162,322429556,1023003875,1328535963,3138645732,
%U A059186 11618168524,137721814936,156929353744,166732460513,813398686532
%N A059186 Engel expansion of Pi^2/6, or zeta(2) = 1.64493.
%C A059186 Cf. A006784 for definition of Engel expansion.
%D A059186 F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H A059186 G. C. Greubel and T. D. Noe, <a href="/A059186/b059186.txt">Table of n, a(n) for n = 1..1000</a>[Terms 1 to 300 computed by T. D. Noe; Terms 301 to 1000 computed by G. C. Greubel, Dec 27 2016]
%H A059186 F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H A059186 P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
%H A059186 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t A059186 EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
%t A059186 NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
%t A059186 EngelExp[N[Pi^2/6, 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)
%Y A059186 Cf. A013661, A053980, A067912.
%K A059186 nonn,easy,nice
%O A059186 1,2
%A A059186 _Mitch Harris_