A322603 Continued fraction for sinh(gamma).

0, 1, 1, 1, 1, 3, 2, 11, 2, 1, 2, 3, 1, 8, 1, 1, 2, 3, 2, 8, 1, 3, 5, 17, 15, 2, 1, 1, 1, 1, 2, 7, 1, 1, 1, 4, 1, 11, 1, 2, 20, 19, 6, 7, 23, 14, 1, 10, 3, 2, 1, 1, 154, 5, 6, 2, 2, 1, 23, 1, 1, 28, 2, 2, 5, 2, 1, 1, 1, 1332, 1, 15, 1, 1, 1, 1, 1, 1, 2, 6, 2, 1, 2, 1, 4, 5, 28, 6, 1

Offset

0,6

Comments

Continued fraction of (exp(gamma)-exp(-gamma))/2 = sinh(gamma) (A147709), where gamma is the Euler-Mascheroni constant (A001620).

See A322602 for the continued fraction of cosh(gamma).

Links

Table of n, a(n) for n=0..88.

Example

0 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(3 + 1/(2 + 1/(11 + ...))))))) = 0.60980646721165640770618044...

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A147709 (decimal expansion), A001620 (Euler-Mascheroni constant), A322602.

Sequence in context: A153187 A248242 A215598 * A152177 A110326 A112061

Adjacent sequences: A322600 A322601 A322602 * A322604 A322605 A322606

Keyword

nonn,cofr

Author

Tristan Cam, Dec 20 2018

Extensions

Offset changed and data corrected by Andrew Howroyd, Jul 05 2024

Status

approved