A244850 Decimal expansion of 'c2', a constant (negated) closely related to 'c1', the Quinn-Rand-Strogatz (QRS) constant of nonlinear physics.

1, 0, 4, 6, 8, 5, 4, 5, 9, 4, 3, 3, 0, 7, 1, 1, 7, 6, 2, 6, 2, 1, 5, 8, 4, 3, 6, 5, 8, 3, 9, 5, 0, 3, 6, 1, 5, 6, 6, 3, 0, 6, 1, 8, 8, 4, 2, 2, 9, 2, 8, 6, 5, 9, 2, 4, 0, 8, 9, 7, 9, 9, 0, 3, 2, 4, 4, 5, 1, 6, 1, 1, 6, 4, 6, 0, 4, 9, 9, 5, 6, 6, 7, 8, 9, 2, 4, 0, 1, 9, 5, 0, 8, 7, 1, 2, 2, 5, 4, 7, 4

Offset

0,3

Links

Table of n, a(n) for n=0..100.

D. H. Bailey and J. M. Borwein, Experimental computation as an ontological game changer, 2014. p. 21.

Eric Weisstein's MathWorld, QRS Constant.

Formula

c2 = c1 - c1^2 - 30*zeta(-1/2, c1/2)/zeta(3/2, c1/2), where zeta is the generalized Riemann zeta function.

Example

-0.104685459433071176262158436583950361566306188422928659240897990324451611646...

Mathematica

digits = 101; c1 = z /. FindRoot[Zeta[1/2, z/2], {z, 1}, WorkingPrecision -> digits+5]; c2 = c1 - c1^2 - 30*Zeta[-1/2, c1/2]/Zeta[3/2, c1/2]; RealDigits[c2, 10, digits] // First

Crossrefs

Cf. A131329.

Sequence in context: A286366 A331059 A201336 * A188930 A332331 A352421

Adjacent sequences: A244847 A244848 A244849 * A244851 A244852 A244853

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 07 2014

Status

approved