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A244662 Decimal expansion of 'C' (as designated by D. Shanks), a constant appearing in the second order term of the asymptotic expansion of the number of non-hypotenuse numbers not exceeding a given bound. 1
7, 0, 4, 7, 5, 3, 4, 5, 1, 7, 0, 5, 9, 4, 7, 8, 8, 4, 1, 2, 2, 5, 5, 8, 1, 9, 7, 5, 9, 1, 8, 9, 8, 8, 1, 8, 5, 2, 1, 5, 9, 9, 7, 6, 4, 5, 4, 9, 2, 3, 5, 8, 3, 1, 6, 1, 7, 4, 4, 5, 4, 8, 8, 3, 4, 1, 3, 6, 2, 8, 4, 6, 3, 9, 0, 3, 1, 8, 8, 4, 4, 4, 6, 0, 6, 3, 6, 4, 9, 2, 5, 3, 5, 2, 2, 3, 0, 2, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 2.3 Landau-Ramanujan Constant, p. 101.

LINKS

Table of n, a(n) for n=0..99.

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

Daniel Shanks, Non-hypotenuse Numbers, Fib. Quart., 13:4 (1975), pp. 319-321.

Eric Weisstein's MathWorld, Lemniscate Constant

FORMULA

C = c + 1/2*log((Pi/L)^2*exp(gamma)/2), where c is A227158 and L the Lemniscate constant A062539.

EXAMPLE

0.70475345170594788412255819759189881852...

MATHEMATICA

digits = 100; 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]; c = A227158 = f[m]; c + 1/2 Log[(Pi/L)^2*Exp[EulerGamma]/2] // RealDigits[#, 10, digits] & // First

CROSSREFS

Cf. A009003, A004144, A062539, A227158, A244659 (first order term).

Sequence in context: A011392 A177156 A016582 * A060708 A021997 A099737

Adjacent sequences:  A244659 A244660 A244661 * A244663 A244664 A244665

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jul 04 2014

STATUS

approved

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Last modified September 23 01:32 EDT 2020. Contains 337291 sequences. (Running on oeis4.)