%I A072829
%S A072829 2,5,9,16,23,32,42,54,68,82,99,116,135,156,178,201,226,252,280,309,340,
%T A072829 372,406,441,477,515,554,595,637,681,726,772,820,869,920,973,1026,1081,
%U A072829 1138,1196,1256,1316,1379,1443,1508,1575,1643,1712,1783,1856,1930,2005
%N A072829 Greatest m such that product{(1 - k/m); k=1,n-1} <= 1/2.
%C A072829 Among n randomly selected dates over an interval of m days (or less), 
               the odds are even (or better than even) for two or more of them to 
               coincide.
%C A072829 Halley's Comet appeared in exactly one year between each of the last 
               9 given entries of this sequence, i.e. a(45) to a(53). - David C. 
               Terr (David_C_Terr(AT)raytheon.com), Jan 03 2005
%F A072829 Corresponds to the ultimate occurrence of n in A033810. For large n, 
               m has magnitude n^2/2ln2.
%e A072829 Thus a(7)=32 for instance implies that among 7 persons bearing the same 
               astrological sign(extending over 30 days or so) the odds are trifle 
               better than even for at least two of them further sharing a common 
               birthday.
%t A072829 f[n_] := (k = 1; While[ Product[1 - i/k, {i, 1, (n - 1)}] <= 1/2, k++ 
               ]; Return[k - 1]); Table[ f[n], {n, 2, 53}]
%Y A072829 Cf. A033810, A064619.
%Y A072829 Sequence in context: A045649 A024519 A160664 this_sequence A138226 A007979 
               A097701
%Y A072829 Adjacent sequences: A072826 A072827 A072828 this_sequence A072830 A072831 
               A072832
%K A072829 nonn
%O A072829 2,1
%A A072829 Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 22 2002
%E A072829 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 23 
               2002
%E A072829 More terms from David C. Terr (David_C_Terr(AT)raytheon.com), Jan 03 
               2005