

A102912


Decimal expansion of a close approximation to the Ramanujan constant.


5



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
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OFFSET

18,1


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.  JeanFrançois Alcover, Jun 22 2015


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


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


EXAMPLE

262537412640768743.999999999999251123875936799800954417367910227716...


MATHEMATICA

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


CROSSREFS

Cf. A060295.
Sequence in context: A221188 A220532 A060295 * A064850 A151853 A268766
Adjacent sequences: A102909 A102910 A102911 * A102913 A102914 A102915


KEYWORD

cons,nonn


AUTHOR

Eric W. Weisstein, Jan 17 2005


STATUS

approved



