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A322545 Continued fraction for cos(gamma). 1

%I #32 Jul 07 2024 10:17:09

%S 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,

%T 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,

%U 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

%N Continued fraction for cos(gamma).

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

%C See A322601 for the continued fraction of imaginary part.

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

%p with(numtheory): cfrac(cos(gamma),100,'quotients'); # _Muniru A Asiru_, Dec 20 2018

%t ContinuedFraction[ Cos[EulerGamma], 100]

%o (PARI) contfrac(cos(Euler)) \\ _Michel Marcus_, Dec 21 2018

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

%K nonn,cofr

%O 0,3

%A _Tristan Cam_, Dec 20 2018

%E Offset changed by _Andrew Howroyd_, Jul 07 2024

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Last modified July 30 22:12 EDT 2024. Contains 374771 sequences. (Running on oeis4.)