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A054404 Number of daughters to wait before picking in sultan's dowry problem. +0
1
0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27 (list; graph; listen)
OFFSET

1,5

COMMENT

The correct rule can be found in the Gardner reference (p. 60) and in the Wikipedia article (see link): if the number of candidates is n, then the optimal r (the number of candidates to skip) is the r that maximizes (r/n)(1/r+1/(r+1)+...+1/(n-1)). - Zvi Mendlowitz (zvi113(AT)zahav.net.il), Jul 12 2007

REFERENCES

M. Gardner, My Best Mathematical and Logic Puzzles, Dover, 1994

LINKS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Anonymous, Secretary problem.

FORMULA

a(n) = the integer r that maximizes (r/n)(1/r+1/(r+1)+...+1/(n-1)) - Zvi Mendlowitz (zvi113(AT)zahav.net.il), Jul 12 2007

CROSSREFS

Sequence in context: A026414 A077219 A026405 this_sequence A008671 A025771 A053265

Adjacent sequences: A054401 A054402 A054403 this_sequence A054405 A054406 A054407

KEYWORD

nonn

AUTHOR

Eric Weisstein (eric(AT)weisstein.com)

EXTENSIONS

Corrected by Zvi Mendlowitz (zvi113(AT)zahav.net.il), Jul 12 2007

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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