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A242015 Decimal expansion of the Euler-Kronecker constant (as named by P. Moree) for non-hypotenuse numbers. 0
4, 0, 9, 5, 0, 6, 9, 0, 3, 4, 1, 1, 8, 9, 5, 7, 6, 8, 2, 4, 5, 1, 1, 6, 3, 9, 5, 1, 8, 3, 7, 9, 7, 6, 3, 7, 0, 4, 3, 1, 9, 9, 5, 2, 9, 0, 9, 8, 4, 7, 1, 6, 6, 3, 2, 3, 4, 8, 9, 0, 9, 7, 6, 6, 8, 2, 7, 2, 5, 6, 9, 2, 7, 8, 0, 6, 3, 7, 6, 8, 8, 9, 2, 1, 2, 7, 2, 9, 8, 5, 0, 7, 0, 4, 4, 6, 0, 5, 2, 8, 7, 7, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constants, p. 99.

LINKS

Table of n, a(n) for n=0..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 11.

Pieter Moree, Counting numbers in multiplicative sets: Landau versus Ramanujan. p. 13, arXiv:1110.0708v1 [math.NT] 4 Oct 2011

D. Shanks, The second-order term in the asymptotic expansion of B(x), Mathematics of Computation 18 (1964), pp. 75-86.

Eric Weisstein's World of Mathematics, Landau-Ramanujan Constant

FORMULA

1 - 2*A244662.

EXAMPLE

-0.40950690341189576824511639518379763704319952909847166323489...

MATHEMATICA

digits = 103; 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] - EulerGamma + Log[Pi] - 4*Log[Gamma[3/4]], 10, digits] // First

CROSSREFS

Cf. A242013, A244662.

Sequence in context: A100074 A330422 A035102 * A187507 A187857 A215499

Adjacent sequences:  A242012 A242013 A242014 * A242016 A242017 A242018

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Aug 11 2014

STATUS

approved

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Last modified December 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)