A059182 - OEIS

%I #30 Apr 13 2018 11:18:05

%S 1,1,4,5,20,30,48,74,265,818,897,2027,5107,6846,13049,236586,364437,

%T 643493,1144424,7294777,49484843,51161394,76008087,202870914,

%U 391981014,11731070977,79069971960,415100034571,1212266245583

%N Engel expansion of log(10) = 2.30259...

%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.

%D .

%H G. C. Greubel, <a href="/A059182/b059182.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@ NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]]; EngelExp[N[Log[10], 7!], 50] (* modified by _G. C. Greubel_, Dec 26 2016 *)

%Y Cf. A002392.

%K nonn,easy,nice

%O 1,3

%A _Mitch Harris_