login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A366166 Decimal expansion of sqrt(Pi)/(3*sqrt(3))*(Gamma(1/3)/Gamma(5/6))^3. 3
4, 5, 5, 9, 7, 9, 4, 4, 9, 9, 9, 5, 9, 8, 4, 5, 8, 1, 5, 4, 8, 1, 7, 3, 6, 4, 8, 4, 5, 5, 7, 2, 4, 8, 1, 1, 7, 6, 3, 6, 7, 4, 2, 3, 8, 0, 1, 6, 6, 1, 4, 0, 5, 6, 3, 5, 0, 5, 1, 8, 3, 8, 7, 6, 5, 4, 7, 2, 1, 1, 5, 9, 5, 9, 3, 5, 5, 7, 0, 4, 4, 9, 2, 3, 2, 4, 8, 7, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This constant c occurs in the probability that the "big player" in a game with 3 gamblers goes broke first, although he starts with an initial capital of N-2 units, whereas the other two gamblers start with one unit each. This probability is ~ c/N^3. See Diaconis link for details.
LINKS
Persi Diaconis, Gambler's ruin with k gamblers (slide 3), talk in the Rutgers Experimental Mathematics Seminar, Fall 2023 Semester, Oct. 12, 2023.
FORMULA
Equals Gamma(1/3)^9 / (2*Pi)^4. - Peter Luschny, Oct 13 2023
EXAMPLE
4.5597944999598458154817364845572481176367423801661405635...
MATHEMATICA
First[RealDigits[Gamma[1/3]^9/(2Pi)^4, 10, 100]] (* Paolo Xausa, Oct 14 2023 *)
PROG
(PARI) sqrt(Pi)/(3*sqrt(3))*(gamma(1/3)/gamma(5/6))^3
CROSSREFS
Sequence in context: A268604 A246823 A088245 * A154857 A019314 A335820
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Oct 13 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)