login
Decimal expansion of A060295^6.
6

%I #30 Dec 14 2019 08:20:02

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

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

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

%N Decimal expansion of A060295^6.

%C A large near-integer obtained by taking the Ramanujan constant e^(Pi*sqrt(163)) to the sixth power. The constants for even higher powers are in general no longer near integers.

%D Henri Cohen, A Course in Computational Algebraic Number Theory, 3., corr. print., Springer-Verlag Berlin Heidelberg New York, 1996 pp. 383.

%H G. C. Greubel, <a href="/A166532/b166532.txt">Table of n, a(n) for n = 105..10000</a>

%H Math Overflow, <a href="http://mathoverflow.net/questions/4775/why-are-powers-of-exppisqrt163-almost-integers">Questions</a>

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>, MathWorld

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

%F Equals exp(6*Pi*sqrt(163)) = A166528^3 = A166529^2.

%e 327451666639079200503292535866541250265248788274691526825971156\

%e 747731856100971255480468836963064283775072.000097175254162592084120177\

%e 65659310106524359922985819691442056333282681...

%t RealDigits[Exp[Pi Sqrt[163]]^6,10,120][[1]] (* _Harvey P. Dale_, Nov 27 2011 *)

%o (PARI) exp(6*sqrt(163)*Pi) \\ _Charles R Greathouse IV_, Nov 05 2014

%Y Cf. A166528, A166529, A166530, A166531.

%K nonn,cons

%O 105,1

%A _Mark A. Thomas_, Oct 16 2009

%E Formula edited and connected to other powers by _R. J. Mathar_, Feb 27 2010

%E Minor edits by _Vaclav Kotesovec_, Jul 04 2014