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A242433 Decimal expansion of one of the Pell-Stevenhagen constants. 0
2, 6, 9, 7, 3, 1, 8, 4, 6, 1, 9, 6, 9, 6, 3, 3, 7, 7, 3, 8, 2, 1, 2, 7, 1, 0, 6, 7, 4, 8, 9, 1, 0, 8, 1, 9, 1, 9, 4, 4, 7, 4, 4, 4, 6, 3, 5, 4, 0, 4, 4, 6, 4, 2, 4, 8, 1, 8, 1, 7, 6, 7, 0, 0, 1, 7, 2, 5, 8, 5, 6, 9, 1, 1, 3, 0, 9, 7, 5, 9, 0, 5, 4, 9, 5, 1, 2, 0, 7, 2, 5, 2, 0, 0, 4, 7, 7, 3, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

P. Stevenhagen conjectured that the asymptotic counting function of the squarefree integers for which the negative Pell equation x^2 - n*y^2 = -1 has an integer solution, was f(n) ~ (6/Pi^2)*P*K*n/sqrt(log(n)).

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 119.

LINKS

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

Eric Weisstein's MathWorld, Landau-Ramanujan Constant

Eric Weisstein's MathWorld, Pell Constant

FORMULA

(6/Pi^2)*P*K where P is the Pell constant 0.5805775582... and K the Landau-Ramanujan constant 0.7642236535...

EXAMPLE

0.26973184619696337738212710674891...

MATHEMATICA

(* After Victor Adamchik *) LandauRamanujan[n_] := With[{K = Ceiling[Log[2, n*Log[3, 10]]]}, N[Product[(((1 - 2^(-2^k))*4^2^k*Zeta[2^k])/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^2^(-k - 1), {k, 1, K}]/Sqrt[2], n]]; K = LandauRamanujan[100]; P = 1 - QPochhammer[1/2, 1/4]; RealDigits[6/Pi^2*P*K, 10, 100] // First

CROSSREFS

Cf. A064533, A141848.

Sequence in context: A155678 A134946 A175575 * A011046 A246828 A136701

Adjacent sequences:  A242430 A242431 A242432 * A242434 A242435 A242436

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 14 2014

STATUS

approved

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Last modified June 24 17:50 EDT 2019. Contains 324330 sequences. (Running on oeis4.)