A100378 Decimal expansion of exp(Pi*sqrt(89/3)).

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

Offset: 8

Author

Gerald McGarvey, Dec 29 2004

Keywords

• nonn
• cons

Comments

Let q = this constant, then q = 300^3 + Sum_{k=0...infinity} (-1)^i*A030197(i)/q^i where A030197 is the McKay-Thompson series of class 3A for Monster, expansion of Hauptmodul for X_0^{+}(3) and expansion of (h+27)^2/h, where h = (eta(q)/eta(q^3))^12.

Examples

			27000041.999971000057006717059989970669906272703208212...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 8..10000
• Titus Piezas III, Pi Formulas

Crossrefs

Cf. A030197, A007243, A045480, A060295.

Programs

Magma

R:= RealField(); Exp(Pi(R)*Sqrt(89/3)); // G. C. Greubel, Feb 14 2018

Mathematica

RealDigits[Exp[Pi*Sqrt[89/3]], 10, 100][[1]] (* G. C. Greubel, Feb 14 2018 *)

PARI

exp(Pi*sqrt(89/3)) \\ G. C. Greubel, Feb 14 2018