A266296 - OEIS

%I #27 Mar 13 2016 10:06:24

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

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

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

%N Decimal expansion of a number close to 24, related to the Ramanujan number e^(Pi*sqrt(163)).

%H Tito Piezas III <a href="https://sites.google.com/site/tpiezas/Home">The Ramanujan pages</a>, see section 22.

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

%F x^24 - e^(Pi*sqrt(163)), where x is the real root of x^3 - 6x^2 + 4x - 2.

%e 24.00000000000000105127873861411207506351157289072577264955435...

%t QP = QPochhammer; r4A[tau_] := With[{q = Exp[2 I Pi tau]}, (1/q) (QP[q^2]^2/(QP[q] QP[q^4]))^24]; RealDigits[r4A[(1/2) Sqrt[-163]] - Exp[Pi Sqrt[163]], 10, 105][[1]]

%t (* or: *)

%t x = Root[#^3 - 6#^2 + 4# - 2&, 1]; RealDigits[x^24 - Exp[Pi Sqrt[ 163]], 10, 105][[1]]

%Y Cf. A060295, A097340, A114609, A114610.

%K nonn,cons

%O 2,1

%A _Jean-François Alcover_, Mar 13 2016