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Engel expansion of gamma^2, (gamma is the Euler-Mascheroni constant A001620) = 0.333178.
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%I #23 Apr 13 2018 11:22:04

%S 4,4,4,4,4,6,23,26,126,132,154,269,421,911,1899,7335,14245,34244,

%T 78354,173699,239896,247397,659900,1646344,2454988,6831657,65833355,

%U 839918922,1187969748,3583279448,4114383765,6590212761,11304687651

%N Engel expansion of gamma^2, (gamma is the Euler-Mascheroni constant A001620) = 0.333178.

%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 G. C. Greubel, <a href="/A059190/b059190.txt">Table of n, a(n) for n = 1..1000</a>

%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@

%t NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];

%t EngelExp[N[EulerGamma^2, 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)

%Y Cf. A155969.

%K nonn,easy,nice

%O 1,1

%A _Mitch Harris_