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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Cf. A006784 for definition of Engel expansion.

LINKS

Table of n, a(n) for n=1..32.

Greg Egan, Puzzle in which this value arises naturally

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)

Wikipedia, Engel Expansion

Eric Weisstein's World of Mathematics, Engel Expansion

Index entries for sequences related to Engel expansions

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: A047591 A239869 A289547 * A187922 A032456 A228442

Adjacent sequences:  A329907 A329909 A329910 * A329913 A329914 A329915

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 23 2019

STATUS

approved

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Last modified February 24 10:11 EST 2020. Contains 332209 sequences. (Running on oeis4.)