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A256843 Decimal expansion of the generalized Euler constant gamma(2,3). 12
0, 7, 3, 2, 0, 7, 3, 7, 5, 7, 0, 6, 1, 5, 9, 5, 9, 3, 6, 6, 9, 0, 3, 1, 8, 5, 9, 9, 0, 7, 5, 2, 9, 1, 3, 9, 0, 7, 4, 6, 2, 3, 8, 3, 0, 2, 6, 8, 3, 0, 9, 3, 4, 5, 6, 2, 9, 3, 9, 0, 6, 4, 4, 6, 6, 9, 8, 5, 1, 0, 9, 4, 2, 7, 4, 5, 9, 7, 4, 0, 4, 1, 7, 7, 2, 3, 0, 8, 1, 5, 5, 3, 0, 8, 6, 0, 9, 0, 3, 1, 6, 0, 1, 6, 8, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.
FORMULA
Equals EulerGamma/3 - Pi/(6*sqrt(3)) + log(3)/6.
Equals -(psi(2/3) + log(3))/3 = (A200064 - A002391)/3. - Amiram Eldar, Jan 07 2024
EXAMPLE
0.07320737570615959366903185990752913907462383026830934562939...
MATHEMATICA
Join[{0}, RealDigits[-Log[3]/3 - PolyGamma[2/3]/3, 10, 105] // First]
PROG
(PARI) default(realprecision, 100); Euler/3 - Pi/(6*sqrt(3)) + log(3)/6 \\ G. C. Greubel, Aug 28 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/3 - Pi(R)/(6*Sqrt(3)) + Log(3)/6; // G. C. Greubel, Aug 28 2018
CROSSREFS
Cf. A001620 (gamma(1,1) = EulerGamma), A002391, A200064.
Primitive ruler-and-compass constructible gamma(r,k): A228725 (1,2), A256425 (1,3), A256778 (1,4), A256779 (1,5), A256780 (2,5), A256781 (1,8), A256782 (3,8), A256783 (1,12), A256784 (5,12).
Other gamma(r,k) (1 <= r <= k <= 5): A239097 (2,2), A256843 (2,3), A256844 (3,3), A256845 (2,4), A256846 (3,4), A256847 (4,4), A256848 (3,5), A256849 (4,5), A256850 (5,5).
Sequence in context: A160390 A002194 A355674 * A033327 A024584 A132713
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)