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

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, 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, 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

Offset

1,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller's coin tossing constants, p. 339.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Run

Wikipedia, Feller's coin-tossing constants

Formula

Equals -2/3 - 4/(3*(17 + 3*sqrt(33))^(1/3)) + 2*(17 + 3*sqrt(33))^(1/3)/3. - Vaclav Kotesovec, Oct 14 2018

Positive real root of x^3 + 2*x^2 + 4*x - 8. - Peter Luschny, Oct 14 2018

Equals 2/A058265 = 2*A192918. - Jon Maiga, Nov 24 2018

Example

1.0873780253841527231417119436....

Maple

evalf[120](solve(x^3+2*x^2+4*x-8=0, x)[1]); # Muniru A Asiru, Nov 25 2018

Mathematica

alpha = Root[1-x+(x/2)^4, x, 1]; RealDigits[alpha, 10, 102] // First (* Jean-François Alcover, Jun 03 2014 *)

Prog

(PARI) solve(x=1, 3/2, 1-x+(x/2)^4) \\ Michel Marcus, Oct 14 2018

Crossrefs

Cf. A086254, A058265, A192918.

Sequence in context: A182499 A358943 A198561 * A225119 A094883 A131081

Adjacent sequences: A086250 A086251 A086252 * A086254 A086255 A086256

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 13 2003

Status

approved