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%I #4 Dec 07 2016 16:31:54
%S 1,4,4,6,6,27,74,86,372,853,947,1475,3686,9084,19174,30737,1530833,
%T 2401466,2521253,3649563,3802245,9320024,1092256819,2114664794,
%U 2878948610,8842525055,13769551820,26996892389,215947176106,269439735691,13694290818678,18312336654245,19649485782723,63266709043539
%N Engel expansion of plastic constant (real root of x^3 - x - 1).
%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/PlasticConstant.html">Plastic Constant</a>
%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%e (1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3) = 1.324717957244... = 1/1 + 1/(1*4) + 1/(1*4*4) + 1/(1*4*4*6) + 1/(1*4*4*6*6) + 1/(1*4*4*6*6*27) + ...
%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[(1/2 + Sqrt[23/108])^(1/3) + (1/2 - Sqrt[23/108])^(1/3), 7! ], 40]
%Y Cf. A006784 (for definition of Engel expansion).
%Y Cf. A060006, A072117.
%K nonn,easy
%O 1,2
%A _Ilya Gutkovskiy_, Nov 28 2016
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