A102912 Decimal expansion of a close approximation to the Ramanujan constant.

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

Offset: 18

Author

Eric W. Weisstein, Jan 17 2005

Keywords

• cons
• nonn

Comments

First differs from Ramanujan's constant (A060295) at a(33). - Omar E. Pol, Jun 26 2012

Kontsevich & Zagier give also exp(3*log(640320)) = 2.62537412640768000... as a close approximation to the Ramanujan constant. - Jean-François Alcover, Jun 22 2015

Examples

			262537412640768743.999999999999251123875936799800954417367910227716...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 18..10000
• M. Kontsevich and D. Zagier, Periods, Institut des Hautes Etudes Scientifiques 2001 IHES/M/01/22
• Eric Weisstein's World of Mathematics, Ramanujan Constant

Crossrefs

Cf. A060295.

Programs

Mathematica

RealDigits[ Root[ #^3 - 6#^2 + 4# - 2 &, 1]^24 - 24, 10, 111][[1]]

Formula

Equals: Real root of x^3 - 6*x^2 + 4*x - 2 = 0, being x_{real} = (6 + (3*(45 + sqrt(489)))^(1/3) + (3*(45 - sqrt(489)))^(1/3))/3 = 5.31863, evaluated as (x_{real})^24 - 24. - G. C. Greubel, Feb 15 2018