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A329912
Engel expansion of exp(Pi/4).
2
1, 1, 6, 7, 9, 17, 57, 283, 326, 791, 10332, 17303, 24977, 85451, 96025, 192273, 337177, 700071, 1394732, 2514757, 73904827, 176943055, 340834596, 663816066, 833303392, 2045234708, 2352089677, 7248164506, 10106625539, 32495772149, 54837573240, 60139816999
OFFSET
1,3
COMMENTS
Cf. A006784 for definition of Engel expansion.
LINKS
F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
P. Erdős and Jeffrey Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
Grant Sanderson and Brady Haran, Darts in Higher Dimensions, Numberphile video (2019)
Eric Weisstein's World of Mathematics, Engel Expansion
Wikipedia, Engel Expansion
MAPLE
Digits:= 250:
engel:= (r, n)-> `if`(n=0 or r=0, NULL,
[ceil(1/r), engel(r*ceil(1/r)-1, n-1)][]):
engel(evalf(exp(Pi/4)), 32);
CROSSREFS
Cf. A006784, A160510 (decimal expansion), A320428 (continued fraction).
Sequence in context: A340765 A239869 A289547 * A187922 A032456 A228442
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 23 2019
STATUS
approved