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A306480 Numbers k such that A054404(k) is not floor(k/e - 1/(2*e) + 1/2). 0
97, 24586, 14122865, 14437880866, 23075113325617, 53123288947296842, 166496860519928411041, 681661051602157413173890, 3532450008306093939076231361, 22600996284275635202947629995722, 174979114331029936735527491233938577, 1612273088535187752419835130130200398626 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that the optimal threshold in the secretary problem with k candidates is not floor(k/e - 1/(2*e) + 1/2).

LINKS

Table of n, a(n) for n=1..12.

J. P. Gilbert and F. Mosteller, Recognizing the Maximum of a Sequence, Journal of the American Statistical Association, Vol. 61 No. 313 (1966), 35-73.

Eric Weisstein's World of Mathematics, Sultan's Dowry Problem

Wikipedia, Secretary problem

EXAMPLE

A054404(97)=35 but floor(97/e - 1/(2e) + 1/2) = 36.

MATHEMATICA

P[r_, n_] := If[r == 0, 1/n, r/n (PolyGamma[0, n] - PolyGamma[0, r])]

in[n_] := (n - 1/2)/E + 1/2 - (3E - 1)/2/(2 n + 3E - 1) - 1

su[n_] := n/E - 1/2/E + 1/2

A054404[n_] := If[P[Floor[su[n]], n] >= P[Ceiling[in[n]], n], Floor[su[n]], Ceiling[in[n]]]

lista = Select[Range[25000], ! Floor[su[#]] == Ceiling[in[#]] &];

IS[n_] := If[Floor[su[n]] == Ceiling[in[n]], False, ! (A054404[n] == Floor[su[n]])]

Select[lista, IS]

CROSSREFS

Cf. A054404, A226242, A226243, A226082.

Sequence in context: A218318 A233426 A173129 * A321041 A173354 A176135

Adjacent sequences:  A306477 A306478 A306479 * A306481 A306482 A306483

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Feb 18 2019

EXTENSIONS

a(4)-a(12) from Jon E. Schoenfield Feb 28 2019

STATUS

approved

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Last modified October 16 05:32 EDT 2019. Contains 328044 sequences. (Running on oeis4.)