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%I #4 Dec 07 2016 16:31:43
%S 3,3,4,4,4,6,15,48,118,147,671,1026,3075,44641,48364,1868380,75080506,
%T 96848501,911582093,2511879981,8700005050,15888441652,108526838262,
%U 446779835336,632466801279,1084794852728,1184722346307,1657692322844,12376968750845,17341469111712,27996895637798,38935285631573
%N Engel expansion of natural logarithm of golden ratio.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>
%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%e 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 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 Cf. A006784 (for definition of Engel expansion).
%Y Cf. A001622, A002390, A028259, A059195.
%K nonn,easy
%O 1,1
%A _Ilya Gutkovskiy_, Nov 28 2016
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