A322602 Continued fraction for cosh(gamma).

1, 5, 1, 5, 4, 1, 5, 1, 1, 2, 9, 1, 1, 8, 1, 16, 1, 2, 1, 2, 1, 1, 1, 4, 27, 2, 1, 1, 1, 2, 1, 8, 1, 3, 5, 1, 1, 1, 1, 1, 16, 2, 1, 4, 1, 2, 62, 1, 8, 12, 1, 4, 1, 4, 3, 1, 1, 4, 1, 3, 20, 1, 2, 2, 106, 1, 13, 2, 7, 2, 1, 2, 4, 7, 1, 2, 1, 1, 2, 11, 1, 1, 2, 24, 1, 2, 2, 1, 1, 12

Offset

0,2

Comments

Continued fraction of (exp(gamma)+exp(-gamma))/2 = cosh(gamma) (A147708), where gamma is the Euler-Mascheroni constant (A001620).

See A322603 for the continued fraction of sinh(gamma).

Links

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

Example

1 + 1/(5 + 1/(1 + 1/(5 + 1/(4 + 1/(1 + 1/(5 + 1/(1 + ...))))))) = 1.17126595077854157753032365...

Maple

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

Mathematica

ContinuedFraction[ (Exp[EulerGamma] + Exp[ -EulerGamma])/2, 100]

Prog

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

Crossrefs

Cf. A147708 (decimal expansion), A001620 (Euler-Mascheroni constant), A322603.

Sequence in context: A060186 A240995 A122002 * A228639 A073226 A309282

Adjacent sequences: A322599 A322600 A322601 * A322603 A322604 A322605

Keyword

nonn,cofr

Author

Tristan Cam, Dec 20 2018

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024

Status

approved