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

Author

Alois P. Heinz, Nov 23 2019

Keywords

• nonn

Comments

Cf. A006784 for definition of Engel expansion.

Links

• 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

Crossrefs

Cf. A006784, A160510 (decimal expansion), A320428 (continued fraction).

Programs

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);