A322545 Continued fraction for cos(gamma).

0, 1, 5, 5, 1, 4, 8, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 18, 1, 73, 2, 5, 3, 5, 4, 1, 1, 1, 7, 1, 4, 2, 1, 1, 32, 12, 2, 19, 8, 1, 1, 1, 1, 1, 3, 5, 2, 70, 1, 6, 6, 1, 52, 2, 1, 2, 10, 1, 1, 1, 4, 1, 3, 1, 5, 1, 7, 3, 1, 1, 1, 20, 5, 6, 6, 2, 4, 3, 7, 1, 1, 2, 10, 1, 9, 12, 45, 1, 16, 2

Offset

0,3

Comments

Continued fraction of the real part of exp(i*gamma) = cos(gamma) (A119806), where gamma is the Euler-Mascheroni constant (A001620).

See A322601 for the continued fraction of imaginary part.

Links

Table of n, a(n) for n=0..89.

Example

0 + 1/(1 + 1/(5 + 1/(5 + 1/(1 + 1/(4 + 1/(8 + 1/(1 + ...))))))) = 0.8379852878801965399549928...

Maple

with(numtheory): cfrac(cos(gamma), 100, 'quotients'); # Muniru A Asiru, Dec 20 2018

Mathematica

ContinuedFraction[ Cos[EulerGamma], 100]

Prog

(PARI) contfrac(cos(Euler)) \\ Michel Marcus, Dec 21 2018

Crossrefs

Cf. A119806 (decimal expansion), A001620 (Euler-Mascheroni constant), A322601.

Sequence in context: A236555 A282969 A046095 * A256737 A055183 A198740

Adjacent sequences: A322542 A322543 A322544 * A322546 A322547 A322548

Keyword

nonn,cofr

Author

Tristan Cam, Dec 20 2018

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024

Status

approved