A330156 Decimal expansion of the continued fraction expansion [1; 1/2, 1/3, 1/4, 1/5, 1/6, ...].

1, 7, 5, 1, 9, 3, 8, 3, 9, 3, 8, 8, 4, 1, 0, 8, 6, 6, 1, 2, 0, 3, 9, 0, 9, 7, 0, 1, 5, 1, 1, 4, 5, 3, 8, 7, 9, 2, 5, 0, 3, 9, 8, 0, 0, 6, 8, 0, 5, 7, 4, 1, 5, 6, 3, 6, 4, 0, 4, 7, 0, 9, 5, 0, 1, 3, 9, 9, 8, 2, 8, 8, 7, 0, 4, 3, 7, 1, 0, 9, 9, 5, 1, 3, 4, 5, 1

Offset

1,2

Comments

This constant is formed from the continued fraction [1; 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, ...] the reciprocals of the positive integers, A000027.

Links

Table of n, a(n) for n=1..87.

Wikipedia, Continued Fraction Expansions of Pi

Formula

Equals 2 / (Pi - 2).

Equals 1/arctan(cot(1)). - Daniel Hoyt, Apr 11 2020

Example

1.7519383938841086612039097015114538792503980068057415636404709501399828870437...

Mathematica

First[RealDigits[2/(Pi - 2), 10, 100]] (* Paolo Xausa, Apr 27 2024 *)

Prog

(PARI) 2 / (Pi - 2) \\ Michel Marcus, Dec 05 2019
(PARI) 1/atan(cotan(1)) \\ Daniel Hoyt, Apr 11 2020

Crossrefs

Cf. A000027, A000796, A052119, A073824.

Sequence in context: A154870 A098687 A021137 * A323811 A316334 A196486

Adjacent sequences: A330153 A330154 A330155 * A330157 A330158 A330159

Keyword

nonn,cons

Author

Daniel Hoyt, Dec 03 2019

Status

approved