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A372482
a(n) is the numerator of the probability that the procedure described in A372422 successfully ends with the selection of a single person, starting with n persons.
6
1, 2, 5, 76, 157, 470, 2839, 723752, 24660295, 814014962, 50504034347, 9849242735372, 59103102606341, 7623954457524682, 2686000485322777549, 10353907366994100404464, 5321713809402035561782157, 303330306424081172196809854, 398574373986665618859496010447, 2696377138892109703091196777892892
OFFSET
1,2
COMMENTS
See A372422 for more information.
The probability is somewhat similar to that for a single survivor as in "group Russian roulette" of A372480. However, the mean of the periodic change is higher (approximately 0.721347 instead of 0.4814...), the amplitude is much smaller, and the period is ~log2(n) instead of ~log(n).
EXAMPLE
a(n)/A372483(n): 1, 2/3, 5/7, 76/105, 157/217, 470/651, 2839/3937, 723752/1003935, 24660295/34200719, 814014962/1128623727, 50504034347/70008871793, ...
Approximately 1.0, 0.66667, 0.71429, 0.72381, 0.72350, 0.72197, 0.72111, 0.72092, 0.72105, 0.72125, 0.72139, 0.72146, 0.72147, 0.72144, 0.72139, 0.72135, ...
PROG
(PARI) \\ valid for n > 1
a372482_3(n) = {my (np=n+1, M=matrix(np)); M[1, 1]=M[2, 2]=1;
for (j=3, np, for (k=0, j-1, M[j, k+1]=binomial(j-1, k)/2^(j-1)));
((1/(matid(n-1) - M[3..np, 3..np])) * M[3..np, 1..2])[n-1, 2]};
a372482(n) = if (n<2, 1, numerator(a372482_3(n)))
CROSSREFS
A372483 are the corresponding denominators.
Cf. A372484, A372485 (positions of local extremes).
Sequence in context: A301993 A128297 A183291 * A254405 A216847 A102983
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, May 06 2024
STATUS
approved