A242013 Decimal expansion of the Euler-Kronecker constant (as named by P. Moree) for hypotenuse numbers.

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

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..100.

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*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

Adjacent sequences: A242010 A242011 A242012 * A242014 A242015 A242016

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 11 2014

Status

approved