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%I #28 Sep 04 2023 11:35:20
%S 1,1,2,3,14,33,57,236,6280,7170,172302,24568434,32871132,43231756,
%T 60680523,83128444,720494727,803406064,1804216488,6655647717,
%U 9106036988,14962799365,37839117297,121819278396,262108609568
%N Engel expansion of Gamma(1/3) = 2.6789385....
%C Cf. A006784 for definition of Engel expansion.
%D F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H 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 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 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%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 ] ]
%Y Cf. A006784, A073005.
%K nonn,easy,nice
%O 1,3
%A _Mitch Harris_
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