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A241005 Decimal expansion of gamma', the analog of Euler's constant when 1/x is replaced by 1/(x*log(x)). 1
4, 2, 8, 1, 6, 5, 7, 2, 4, 8, 7, 1, 2, 3, 5, 0, 7, 5, 1, 9, 1, 4, 5, 8, 8, 0, 3, 8, 3, 2, 4, 8, 0, 0, 4, 4, 6, 1, 0, 7, 3, 6, 1, 4, 3, 0, 4, 5, 6, 9, 9, 7, 0, 5, 8, 4, 7, 8, 3, 4, 3, 8, 1, 3, 4, 4, 2, 5, 6, 2, 4, 3, 6, 4, 1, 3, 3, 4, 8, 2, 8, 1, 4, 7, 1, 5, 8, 9, 5, 4, 7, 7, 0, 6, 3, 5, 5, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5.3 Generalized Euler Constants, p. 32.
LINKS
Harold G. Diamond, A number theoretic series of I. Kasara, Pacific J. Math., Volume 111, Number 2 (1984), 283-285.
Eric Weisstein's MathWorld, Euler-Mascheroni Constant
FORMULA
lim_{m -> infinity} ( Sum_{n=2..m} 1/(n*log(n)) - log(log(m)/log(2)) ).
EXAMPLE
0.4281657248712350751914588...
MATHEMATICA
digits = 99; m0 = 10^digits; dm = 10^digits; Clear[g]; g[m_] := g[m] = NSum[1/(n*Log[n]) - (2*n*Log[Log[m]/Log[2]])/(-2 + m + m^2), {n, 2, m}, WorkingPrecision -> 2 digits, NSumTerms -> 1000, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 30}}]; g[m = m0]; g[m = m0 + dm]; While[Print["m = ", m // N // ScientificForm, " ", RealDigits[g[m], 10, digits]]; RealDigits[g[m], 10, digits + 2] != RealDigits[g[m - dm], 10, digits + 2], m = m + dm]; RealDigits[g[m], 10, digits] // First (* updated Apr 19 2016 *)
CROSSREFS
Sequence in context: A348681 A241298 A019953 * A029841 A112143 A112151
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Extended to 99 digits by Jean-François Alcover, Apr 19 2016
STATUS
approved

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)