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A329912 Engel expansion of exp(Pi/4).

%I A329912 #17 Feb 16 2025 08:33:58
%S A329912 1,1,6,7,9,17,57,283,326,791,10332,17303,24977,85451,96025,192273,
%T A329912 337177,700071,1394732,2514757,73904827,176943055,340834596,663816066,
%U A329912 833303392,2045234708,2352089677,7248164506,10106625539,32495772149,54837573240,60139816999
%N A329912 Engel expansion of exp(Pi/4).
%C A329912 Cf. A006784 for definition of Engel expansion.
%H A329912 Greg Egan, <a href="https://twitter.com/gregeganSF/status/1160461092973211648">Puzzle in which this value arises naturally</a>
%H A329912 F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbrüchen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H A329912 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 A329912 Grant Sanderson and Brady Haran, <a href="https://www.youtube.com/watch?v=6_yU9eJ0NxA">Darts in Higher Dimensions</a>, Numberphile video (2019)
%H A329912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A329912 Wikipedia, <a href="https://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%H A329912 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%p A329912 Digits:= 250:
%p A329912 engel:= (r, n)-> `if`(n=0 or r=0, NULL,
%p A329912         [ceil(1/r), engel(r*ceil(1/r)-1, n-1)][]):
%p A329912 engel(evalf(exp(Pi/4)), 32);
%Y A329912 Cf. A006784, A160510 (decimal expansion), A320428 (continued fraction).
%K A329912 nonn
%O A329912 1,3
%A A329912 _Alois P. Heinz_, Nov 23 2019