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

Author

Tristan Cam, Dec 20 2018

Keywords

• nonn
• cofr

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).

Examples

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024