cp's OEIS Frontend

A182009 a(n) = ceiling(sqrt(2n*log(2))+(3-2*log(2))/6).

%I A182009 #19 Aug 24 2015 04:47:33
%S A182009 2,2,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,
%T A182009 8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,
%U A182009 10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11
%N A182009 a(n) = ceiling(sqrt(2n*log(2))+(3-2*log(2))/6).
%C A182009 This sequence approximates the sequence of solutions to the Birthday Problem, A033810. The two sequences agree for almost all n, i.e., on a set of integers n with density 1.
%H A182009 Gheorghe Coserea, <a href="/A182009/b182009.txt">Table of n, a(n) for n = 1..10000</a>
%H A182009 D. Brink, <a href="http://dx.doi.org/10.1007/s11139-011-9343-9">A (probably) exact solution to the Birthday Problem</a>, Ramanujan Journal, 2012, pp 223-238.
%p A182009 seq(ceil((2*n*log(2))^(1/2) + (3-2*log(2))/6), n=1..1000); # _Robert Israel_, Aug 23 2015
%t A182009 Table[Ceiling[Sqrt[2 n Log[2] + (3 - 2 Log[2])/6]], {n, 82}] (* _Michael De Vlieger_, Aug 24 2015 *)
%o A182009 (PARI)
%o A182009 a(n) = { ceil((2*n*log(2))^(1/2) + (3-2*log(2))/6) };
%o A182009 apply(n->a(n), vector(84, i, i))  \\ _Gheorghe Coserea_, Aug 23 2015
%Y A182009 Approximates A033810.
%K A182009 nonn
%O A182009 1,1
%A A182009 _David Brink_, Apr 06 2012