A086254 Decimal expansion of Feller's beta coin-tossing constant.

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

Offset

1,2

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 (22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33. - Vaclav Kotesovec, Oct 14 2018

Positive real root of 11*x^3 - 22*x^2 + 12*x - 2. - Peter Luschny, Oct 14 2018

Equals 2/(5 - A058265^2). - Jon Maiga, Nov 25 2018

Example

1.2368398446387851018906608761421232....

Maple

evalf[120](solve(11*x^3-22*x^2+12*x-2=0, x)[1]); # Muniru A Asiru, Nov 25 2018

Mathematica

alpha = Root[1-x+(x/2)^4, x, 1]; beta = (2-alpha)/(4-3*alpha); RealDigits[beta, 10, 102] // First (* Jean-François Alcover, Jun 03 2014 *)

Prog

(PARI) default(realprecision, 100); (22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33 \\ G. C. Greubel, Nov 25 2018
(Magma) SetDefaultRealField(RealField(100)); (22 + (847 - 33*Sqrt(33))^(1/3) + (11*(77 + 3*Sqrt(33)))^(1/3))/33; // G. C. Greubel, Nov 25 2018
(Sage) numerical_approx((22 + (847 - 33*sqrt(33))^(1/3) + (11*(77 + 3*sqrt(33)))^(1/3))/33, digits=100) # G. C. Greubel, Nov 25 2018

Crossrefs

Cf. A086253, A058265.

Sequence in context: A302090 A088414 A133441 * A265297 A140266 A140265

Adjacent sequences: A086251 A086252 A086253 * A086255 A086256 A086257

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 13 2003

Status

approved