A266296 Decimal expansion of a number close to 24, related to the Ramanujan number e^(Pi*sqrt(163)).

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, 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, 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

Offset

2,1

Links

Table of n, a(n) for n=2..106.

Tito Piezas III The Ramanujan pages, see section 22.

Eric Weisstein's MathWorld, Almost Integer

Index entries for transcendental numbers.

Formula

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

Example

24.00000000000000105127873861411207506351157289072577264955435...

Mathematica

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]]
(* Alternative: *)
x = Root[#^3 - 6#^2 + 4# - 2&, 1]; RealDigits[x^24 - Exp[Pi Sqrt[ 163]], 10, 105][[1]]

Prog

(PARI) polrootsreal(x^3 - 6*x^2 + 4*x - 2)[1]^24 - exp(Pi*sqrt(163)) \\ Charles R Greathouse IV, Jul 09 2026

Crossrefs

Cf. A060295, A097340, A114609, A114610.

Sequence in context: A321406 A383856 A166926 * A028573 A138758 A107501

Adjacent sequences: A266293 A266294 A266295 * A266297 A266298 A266299

Keyword

nonn,cons,changed

Author

Jean-François Alcover, Mar 13 2016

Status

approved