A320428 Continued fraction expansion of exp(Pi/4).

2, 5, 5, 1, 3, 25, 1, 1, 17, 1, 3, 3, 1, 12, 1, 8, 5, 3, 1, 46, 3, 4, 12, 1, 5, 22, 3, 2, 1, 7, 4, 2, 1, 13, 13, 8, 1, 1, 3, 1, 1, 1, 2, 1, 11, 1, 5, 2, 1, 4, 7, 1, 71, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 4, 6, 1, 9, 1, 1, 1, 6, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 2, 1, 1, 5, 2, 1, 2, 10, 1, 19, 2, 2, 4, 1

Offset: 0

Author

Grant T Sanderson, Aug 28 2019

Keywords

• nonn
• cofr
• easy

Comments

This value arises naturally by taking the ratio of the volume of a unit 2n-dimensional ball to the volume of the 2n-dimensional cube containing it (with side length 2) and summing over all n.

Links

• Greg Egan, Puzzle in which this value arises naturally
• Grant Sanderson and Brady Haran, Darts in Higher Dimensions, Numberphile video (2019)

Crossrefs

Cf. A160510 (decimal expansion), A058287, A087299, A329912 (Engel expansion).

Programs

Mathematica

ContinuedFraction[Exp[Pi/4], 100]

PARI

contfrac(exp(Pi/4)) \\ Felix Fröhlich, Aug 28 2019