A329912 Engel expansion of exp(Pi/4).

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

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)

Eric Weisstein's World of Mathematics, Engel Expansion

Wikipedia, 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: A340765 A239869 A289547 * A187922 A032456 A228442

Adjacent sequences: A329909 A329910 A329911 * A329913 A329914 A329915

Keyword

nonn

Author

Alois P. Heinz, Nov 23 2019

Status

approved