A246771 Decimal expansion of the success probability associated with the optimal stopping problem on patterns in random binary strings.

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

Offset

0,1

Links

Table of n, a(n) for n=0..103.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 46.

Formula

p = (2/135)*exp(-beta)*(4 - 45*beta^2 + 45*beta^3), where beta = A246770 = the largest root of 45*x^3 - 180*x^2 + 90*x + 4.

Example

0.619252270984884908663280718193752667423088771902409501034...

Mathematica

beta = Root[45x^3 - 180*x^2 + 90*x + 4, x, 3]; p = (2/135)*Exp[-beta]*(4 - 45*beta^2 + 45*beta^3); RealDigits[p, 10, 104] // First

Crossrefs

Cf. A246770.

Sequence in context: A117236 A349141 A358968 * A176397 A245724 A021908

Adjacent sequences: A246768 A246769 A246770 * A246772 A246773 A246774

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 03 2014

Status

approved