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

%I A100378 #13 Sep 26 2023 09:52:49
%S A100378 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,
%T A100378 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,
%U A100378 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
%N A100378 Decimal expansion of exp(Pi*sqrt(89/3)).
%C A100378 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.
%H A100378 G. C. Greubel, <a href="/A100378/b100378.txt">Table of n, a(n) for n = 8..10000</a>
%H A100378 Titus Piezas III, <a href="https://sites.google.com/view/tpiezas/0010-article-0-pi-formulas-1">Pi Formulas</a>
%e A100378 27000041.999971000057006717059989970669906272703208212...
%t A100378 RealDigits[Exp[Pi*Sqrt[89/3]], 10, 100][[1]] (* _G. C. Greubel_, Feb 14 2018 *)
%o A100378 (PARI) exp(Pi*sqrt(89/3)) \\ _G. C. Greubel_, Feb 14 2018
%o A100378 (Magma) R:= RealField(); Exp(Pi(R)*Sqrt(89/3)); // _G. C. Greubel_, Feb 14 2018
%Y A100378 Cf. A030197, A007243, A045480, A060295.
%K A100378 nonn,cons
%O A100378 8,1
%A A100378 _Gerald McGarvey_, Dec 29 2004