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A119806 Decimal expansion of cos(gamma). 3
8, 3, 7, 9, 8, 5, 2, 8, 7, 8, 8, 0, 1, 9, 6, 5, 3, 9, 9, 5, 4, 9, 9, 2, 8, 6, 1, 2, 5, 8, 9, 4, 9, 7, 2, 4, 8, 0, 8, 6, 5, 9, 2, 0, 1, 3, 2, 4, 1, 7, 6, 6, 5, 7, 9, 0, 4, 1, 1, 7, 8, 9, 3, 5, 5, 6, 7, 7, 6, 9, 3, 6, 8, 8, 8, 0, 2, 6, 2, 2, 2, 3, 2, 7, 5, 4, 9, 4, 1, 4, 6, 8, 6, 5, 4, 2, 1, 9, 1, 7, 5, 6, 8, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This is the real part of exp(i*gamma), where gamma is the Euler-Mascheroni constant A001620. See A119807 for the imaginary part. The constant exp(gamma) (A073004) appears in many formulas. Does exp(i*gamma)?
LINKS
D. M. Bătineţu-Giurgiu and Neculai Stanciu, Problem UP.328, Romanian Mathematical Magazine, Vol. 30, Autumn edition (2021), p. 114; Solutions, by Mokhtar Khassani-Mostaganem and Marian Ursărescu.
D. M. Bătineţu-Giurgiu, Neculai Stanciu, and José Luis Díaz-Barrero, The Last Three Decades of Lalescu Limit, Arhimede Mathematical Journal, Vol. 7, No. 1 (2020), pp. 16-26. See Problem 7, pp. 23-24.
Toyesh Prakash Sharma, The Applications of the Stirling's approximation to find limits, Revista Electronica MateInfo.ro, December 2020, pp. 44-49. See Problem 4, p. 46.
FORMULA
Equals 2 * e * lim_{n->oo) (sin(gamma(n))-sin(gamma))*(n!)^(1/n), where gamma(n) = Sum_{k=1..n} 1/k - log(n) (Bătineţu-Giurgiu, 2021). - Amiram Eldar, Apr 02 2022
EXAMPLE
0.8379852878801965399549928612589497248086592013241766579...
MATHEMATICA
RealDigits[Cos[EulerGamma], 10, 150][[1]]
PROG
(PARI) default(realprecision, 100); cos(Euler) \\ G. C. Greubel, Aug 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Cos(EulerGamma(R)) // G. C. Greubel, Aug 30 2018
CROSSREFS
Cf. A001620 (Euler-Mascheroni constant), A073004, A119807.
Sequence in context: A099284 A061444 A011214 * A248296 A217732 A089260
KEYWORD
cons,nonn
AUTHOR
T. D. Noe, May 24 2006
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)