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A086253 Decimal expansion of Feller's alpha coin-tossing constant.

%I A086253 #29 Feb 16 2025 08:32:50
%S A086253 1,0,8,7,3,7,8,0,2,5,3,8,4,1,5,2,7,2,3,1,4,1,7,1,1,9,4,3,6,0,3,4,9,5,
%T A086253 9,7,3,0,5,0,4,0,6,5,9,5,3,0,1,9,6,7,8,7,0,4,8,1,6,0,8,0,7,5,6,6,2,3,
%U A086253 3,7,3,4,7,8,5,5,9,4,7,7,3,2,9,7,0,3,1,5,8,2,9,1,5,2,1,1,8,2,5,0,9,2
%N A086253 Decimal expansion of Feller's alpha coin-tossing constant.
%D A086253 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller's coin tossing constants, p. 339.
%H A086253 G. C. Greubel, <a href="/A086253/b086253.txt">Table of n, a(n) for n = 1..10000</a>
%H A086253 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Run.html">Run</a>
%H A086253 Wikipedia, <a href="https://en.wikipedia.org/wiki/Feller%27s_coin-tossing_constants">Feller's coin-tossing constants</a>
%F A086253 Equals -2/3 - 4/(3*(17 + 3*sqrt(33))^(1/3)) +  2*(17 + 3*sqrt(33))^(1/3)/3. - _Vaclav Kotesovec_, Oct 14 2018
%F A086253 Positive real root of x^3 + 2*x^2 + 4*x - 8. - _Peter Luschny_, Oct 14 2018
%F A086253 Equals 2/A058265 = 2*A192918. - _Jon Maiga_, Nov 24 2018
%e A086253 1.0873780253841527231417119436....
%p A086253 evalf[120](solve(x^3+2*x^2+4*x-8=0,x)[1]); # _Muniru A Asiru_, Nov 25 2018
%t A086253 alpha = Root[1-x+(x/2)^4, x, 1]; RealDigits[alpha, 10, 102] // First (* _Jean-François Alcover_, Jun 03 2014 *)
%o A086253 (PARI) solve(x=1, 3/2, 1-x+(x/2)^4) \\ _Michel Marcus_, Oct 14 2018
%Y A086253 Cf. A086254, A058265, A192918.
%K A086253 nonn,cons
%O A086253 1,3
%A A086253 _Eric W. Weisstein_, Jul 13 2003