The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054404 Number of daughters to wait before picking in sultan's dowry problem with n daughters. 15
 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; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 R. J. Mathar, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Sultan's Dowry Problem. Wikipedia, 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 MAPLE A054404 := proc(n)     local r ;     r := 0 ;     sr := 0 ;     for s from 1 to n do         p := s/n*add(1/i, i=s..n-1) ;         if p > sr then             r := s ;             sr := p ;         end if;     end do;     return r; end proc: # R. J. Mathar, Jun 09 2013 MATHEMATICA a[n_] := r /. Last[ Maximize[ {(r/n)*Sum[1/k, {k, r, n - 1}], 0 <= r < n/2}, r, Integers]]; a = 0; a = 1; Table[a[n], {n, 1, 75}] (* Jean-François Alcover, Dec 13 2011, after Zvi Mendlowitz *) (* The code above may not work in Mma 8 *) PR[n_, r_] := (r/n)*Sum[1/k, {k, r, n - 1}]; maxi[li_] := {Do[If[li[[n + 1]] <         li[[n]], aux = n; Break[]], {n, 1, Length[li] - 1}], aux}[]; SEQ = 0; SEQ = 1; SEQ[n_] := maxi[Table[PR[n, i], {i, 1, n - 1}]]; Table[SEQ[n], {n, 1, 133}]  (* José María Grau Ribas, May 11 2013 *) a=0; a=1; a[n_] := Block[{r}, r /. Last@ Maximize[{(r/n) * (PolyGamma[0, n] - PolyGamma[0, r]), 1 <= r < n/2}, r, Integers]]; Array[a, 75] (* Giovanni Resta, May 11 2013 *) CROSSREFS Sequence in context: A077219 A026405 A226033 * A334415 A307152 A008671 Adjacent sequences:  A054401 A054402 A054403 * A054405 A054406 A054407 KEYWORD nonn AUTHOR EXTENSIONS Corrected by Zvi Mendlowitz (zvi113(AT)zahav.net.il), Jul 12 2007 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.

Last modified September 27 19:37 EDT 2022. Contains 357063 sequences. (Running on oeis4.)