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A242013
Decimal expansion of the Euler-Kronecker constant (as named by P. Moree) for hypotenuse numbers.
1
1, 6, 3, 8, 9, 7, 3, 1, 8, 6, 3, 4, 5, 8, 1, 5, 9, 5, 8, 5, 6, 2, 9, 9, 7, 6, 9, 0, 0, 4, 7, 3, 5, 1, 1, 8, 6, 0, 9, 6, 6, 5, 7, 4, 6, 1, 4, 3, 5, 4, 5, 0, 4, 3, 6, 4, 6, 8, 4, 2, 5, 9, 8, 5, 3, 0, 5, 0, 2, 4, 6, 3, 1, 1, 1, 9, 0, 0, 6, 9, 2, 2, 8, 6, 0, 2, 4, 7, 2, 2, 6, 2, 9, 8, 4, 8, 2, 6, 9, 9, 2
OFFSET
0,2
COMMENTS
130000 digits are available (see Links). - Alessandro Languasco, Mar 27 2024
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constants, p. 99.
FORMULA
1 - 2*A227158.
EXAMPLE
-0.1638973186345815958562997690047351186096657461435450436468425985305...
MATHEMATICA
digits = 101; m0 = 5; dm = 5; beta[x_] := 1/4^x*(Zeta[x, 1/4] - Zeta[x, 3/4]); L = Pi^(3/2)/Gamma[3/4]^2*2^(1/2)/2; Clear[f]; f[m_] := f[m] = 1/2*(1 - Log[Pi*E^EulerGamma/(2*L)]) - 1/4*NSum[Zeta'[2^k]/Zeta[2^k] - beta'[2^k]/beta[2^k] + Log[2]/(2^(2^k) - 1), {k, 1, m}, WorkingPrecision -> digits + 10]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits] != RealDigits[f[m - dm], 10, digits], m = m + dm]; RealDigits[1 - 2*f[m], 10, digits] // First
CROSSREFS
Cf. A227158.
Sequence in context: A198836 A271179 A220085 * A242962 A257938 A153632
KEYWORD
nonn,cons
AUTHOR
STATUS
approved