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!)
A295823 Decimal expansion of x > 0 satisfying e + x + e^x*(2x-3) = 0. 0
5, 7, 0, 5, 5, 6, 5, 2, 8, 2, 9, 5, 1, 9, 6, 4, 7, 6, 8, 2, 5, 1, 3, 1, 0, 1, 5, 1, 3, 3, 3, 7, 4, 7, 8, 6, 8, 7, 7, 3, 8, 6, 9, 0, 8, 7, 9, 2, 2, 3, 0, 8, 5, 8, 4, 7, 9, 1, 0, 2, 8, 7, 7, 9, 1, 9, 2, 7, 4, 9, 7, 2, 7, 6, 1, 5, 6, 8, 9, 5, 2, 3, 6, 9, 8, 8, 0, 2, 9, 7, 5, 2, 5, 5, 7, 2, 4, 4, 0, 9, 2, 6, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Consider the following game: A and B are two players, each having exactly one turn.
A goes first. A chooses random numbers (uniformly distributed in [0,1]) and adds them until he stops. If the sum exceeds 1, A loses and B wins.
If the sum of A's numbers does not exceed 1, then B proceeds as A did, choosing random numbers sequentially until the sum of B's numbers exceeds the sum of A's numbers. If the sum of B's numbers exceeds 1, B loses and A wins; otherwise B wins and A loses.
The optimal strategy for A is to stop as soon as the sum exceeds this constant.
LINKS
EXAMPLE
0.57055652829519647682513101513337478687738690879223085847910287791927497276...
MATHEMATICA
RealDigits[x/.FindRoot[E+x+E^x (-3+2 x)==0, {x, 0.3}, WorkingPrecision-> 120]][[1]]
PROG
(PARI) solve(x=0, 1, exp(1) + x + exp(x)*(2*x-3)) \\ Michel Marcus, Dec 11 2017
CROSSREFS
Sequence in context: A176713 A293506 A011350 * A161018 A197254 A013706
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Mathematica program corrected by Harvey P. Dale, Dec 08 2019
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 September 14 02:27 EDT 2024. Contains 375910 sequences. (Running on oeis4.)