A059183 - OEIS

%I #29 Apr 13 2018 11:18:32

%S 1,3,4,4,5,5,5,6,47,109,935,4763,7821,8895,9889,35798,44347,1146551,

%T 7874944,8043393,27403243,34058912,58098040,68760470,80046897,

%U 560099631,611427977,14235032003,602865059026,813485869378

%N Engel expansion of 1/log(2) = 1.4427...

%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="/A059183/b059183.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[1/Log[2], 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)

%Y Cf. A007525 (1/log(2)).

%K nonn,easy,nice

%O 1,2

%A _Mitch Harris_, May 16 2003