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.
%I A278765 #5 Feb 16 2025 08:33:37
%S A278765 3,3,4,4,4,6,15,48,118,147,671,1026,3075,44641,48364,1868380,75080506,
%T A278765 96848501,911582093,2511879981,8700005050,15888441652,108526838262,
%U A278765 446779835336,632466801279,1084794852728,1184722346307,1657692322844,12376968750845,17341469111712,27996895637798,38935285631573
%N A278765 Engel expansion of natural logarithm of golden ratio.
%H A278765 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A278765 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>
%H A278765 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%e A278765 log(phi) = 0.4812118250596... = 1/3 + 1/(3*3) + 1/(3*3*4) + 1/(3*3*4*4) + 1/(3*3*4*4*4) + 1/(3*3*4*4*4*6) + ...
%t A278765 EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[Log[GoldenRatio], 7! ], 40]
%Y A278765 Cf. A006784 (for definition of Engel expansion).
%Y A278765 Cf. A001622, A002390, A028259, A059195.
%K A278765 nonn,easy
%O A278765 1,1
%A A278765 _Ilya Gutkovskiy_, Nov 28 2016