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A086254 Decimal expansion of Feller's beta coin-tossing constant. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A065536 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

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)