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Decimal expansion of exp(4*Pi*sqrt(163)) (or A060295^4).
5

%I #19 Feb 16 2025 08:33:11

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

%T 6,1,8,2,1,4,4,9,1,7,1,8,0,3,9,4,7,1,3,6,6,3,1,8,7,4,7,4,0,6,3,6,8,7,

%U 9,2,0,0,0,0,0,0,3,0,8,4,6,4,3,2,2,1,2,9,9,8,1,1,8,0,1,8,7,9,9,6,2,0,0,0,1

%N Decimal expansion of exp(4*Pi*sqrt(163)) (or A060295^4).

%C Near-integer obtained by taking Ramanujan's constant e^(Pi*sqrt(163)) to the fourth power.

%D Henri Cohen, 'A Course in Computational Algebraic Number Theory', Springer-Verlag Berlin Heidelberg New-York 1996, p. 383.

%H MathOverflow, <a href="http://mathoverflow.net/questions/4775/why-are-powers-of-exppisqrt163-almost-integers">Why are powers of exp(Pi*sqrt(163)) almost integers?</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Heegner_number">Heegner number</a>

%e exp^(4*Pi*sqrt(163)) = 47507787308251777254639209489097266182144917180394713663187474063...

%t RealDigits[Exp[Pi Sqrt[163]]^4,10,120][[1]] (* _Harvey P. Dale_, Apr 20 2011 *)

%o (PARI) exp(4*Pi*sqrt(163)) \\ _Charles R Greathouse IV_, Nov 12 2014

%Y Cf. A166528, A166529, A166531, A166532.

%K nonn,cons,changed

%O 70,1

%A _Mark A. Thomas_, Oct 16 2009