A322601 Continued fraction for sin(gamma).

0, 1, 1, 4, 1, 33, 1, 6, 2, 5, 1, 22, 1, 261, 1, 5, 1, 4, 1, 45, 1, 4, 2, 9, 1, 2, 3, 7, 1, 2, 1, 2, 6, 1, 1, 2, 2, 1, 5, 5, 5, 1, 1, 2, 1, 1, 7, 1, 7, 2, 2, 1, 3, 9, 11, 9, 4, 1, 8, 1, 1, 1, 5, 1, 22, 1, 1, 1, 2, 1, 7, 5, 1, 1, 16, 2, 5, 2, 1, 1, 2, 1, 1, 1, 7, 2, 4, 2, 1, 1, 1, 24

Offset

0,4

Comments

Continued fraction of the imaginary part of exp(i*gamma) = sin(gamma) (A119807), where gamma is the Euler-Mascheroni constant (A001620).

See A322545 for the continued fraction of the real part.

Links

Table of n, a(n) for n=0..91.

Example

0 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + 1/(33 + 1/(1 + 1/(6 + ...))))))) = 0.5456928232039927881573565...

Maple

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

Mathematica

ContinuedFraction[ Sin[EulerGamma], 100]

Prog

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

Crossrefs

Cf. A119807 (decimal expansion), A001620 (Euler-Mascheroni constant), A322545.

Sequence in context: A370136 A051142 A266240 * A374258 A075804 A059844

Adjacent sequences: A322598 A322599 A322600 * A322602 A322603 A322604

Keyword

nonn,cofr

Author

Tristan Cam, Dec 20 2018

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024

Status

approved