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A110617 The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter's million dollar game). 1
0, 0, 0, 0, 1, 5, 4, 9, 6, 1, 8, 7, 9, 3, 7, 7, 6, 7, 3, 0, 9, 2, 4, 1, 9, 2, 6, 4, 8, 6, 0, 8, 4, 4, 2, 3, 2, 3, 1, 8, 8, 4, 9, 5, 6, 3, 0, 0, 7, 5, 0, 0, 1, 5, 4, 9, 6, 1, 8, 7, 9, 3, 7, 7, 6, 7, 3, 0, 9, 2, 4, 1, 9, 2, 6, 4, 8, 6, 0, 8, 4, 4, 2, 3, 2, 3, 1, 8, 8, 4, 9, 5, 6, 3, 0, 0, 7, 5, 0, 0, 1, 5, 4, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Constants such as this one and .64532 have importance with respect to the efficient usage of resources of various types and the minimization of opportunity costs: According to the Mero source, if 100000 players are considering entering Hofstadter's/Scientific American's million dollar game, an optimal mixed strategy for maximizing the magazine's expected loss -- thus maximizing the expected gain for the common good of all 100000 players -- is for each player to preselect an integer from 1 through 64532 and roll a 64532-sided die. A player should enter the game if and only if that player rolls his or her preselected number, which, of course will occur with probability 1/64532. (With instead a 100000-sided die the probability that no one enters is "about 37%" (Mero).). The game pay-out to the single randomly-selected winner from the pool of entrants is defined to be inversely proportional to the number of entrants: 1000000 if one entry, 500000 if two entries, etc.

REFERENCES

Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, Springer-Verlag New York, Inc., 1998, pp. 15-21.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

EXAMPLE

.0000154961879377673092419264860844232318849563007500154961879377673092419...

MATHEMATICA

Join[{0, 0, 0, 0}, RealDigits[1/64532, 10, 96][[1]]] (* G. C. Greubel, Sep 01 2017 *)

CROSSREFS

Sequence in context: A198609 A332794 A054508 * A234356 A338502 A102081

Adjacent sequences: A110614 A110615 A110616 * A110618 A110619 A110620

KEYWORD

cons,nonn

AUTHOR

Rick L. Shepherd, Jul 31 2005

STATUS

approved

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Last modified December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)