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

%I A102912 #22 Feb 16 2025 08:32:56
%S A102912 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,
%T A102912 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,
%U A102912 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
%N A102912 Decimal expansion of a close approximation to the Ramanujan constant.
%C A102912 First differs from Ramanujan's constant (A060295) at a(33). - _Omar E. Pol_, Jun 26 2012
%C A102912 Kontsevich & Zagier give also exp(3*log(640320)) = 2.62537412640768000... as a close approximation to the Ramanujan constant. - _Jean-François Alcover_, Jun 22 2015
%H A102912 G. C. Greubel, <a href="/A102912/b102912.txt">Table of n, a(n) for n = 18..10000</a>
%H A102912 M. Kontsevich and D. Zagier, <a href="http://www.ihes.fr/~maxim/TEXTS/Periods.pdf">Periods</a>, Institut des Hautes Etudes Scientifiques 2001 IHES/M/01/22
%H A102912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanConstant.html">Ramanujan Constant</a>
%F A102912 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
%e A102912 262537412640768743.999999999999251123875936799800954417367910227716...
%t A102912 RealDigits[ Root[ #^3 - 6#^2 + 4# - 2 &, 1]^24 - 24, 10, 111][[1]]
%Y A102912 Cf. A060295.
%K A102912 cons,nonn
%O A102912 18,1
%A A102912 _Eric W. Weisstein_, Jan 17 2005