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A088141 a(n) = the largest k such that, if k samples are taken from a group of n items, with replacement, a duplication is unlikely (p<1/2). 7

%I

%S 1,2,2,2,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,

%T 7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,

%U 10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11

%N a(n) = the largest k such that, if k samples are taken from a group of n items, with replacement, a duplication is unlikely (p<1/2).

%C Related to the birthday paradox. This is essentially the same as A033810.

%H Arkadiusz Wesolowski, <a href="/A088141/b088141.txt">Table of n, a(n) for n = 2..10000</a>

%e a(365)=22 because if 22 people are sampled, it is unlikely that two have the same birthday; but if 23 are sampled, it is likely.

%t lst = {}; s = 1; Do[Do[If[Product[(n - i)/n, {i, j}] <= 1/2, If[j > s, s = j]; AppendTo[lst, j]; Break[]], {j, s, s + 1}], {n, 2, 86}]; lst (* _Arkadiusz Wesolowski_, Apr 29 2012 *)

%Y Cf. A033810, A072829.

%K nonn

%O 2,2

%A Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Nov 06 2003

%E Edited by _Don Reble_, Nov 07 2005

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Last modified September 28 09:35 EDT 2020. Contains 337394 sequences. (Running on oeis4.)