%I #21 Sep 08 2022 08:45:54

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

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

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

%N a(n) = ceiling(sqrt(2*n*log(2))).

%C This sequence approximates the sequence of solutions to the Birthday Problem, A033810. The two sequences agree on a set of integers n with density (3+2 log 2)/6 = 0.731...

%H Gheorghe Coserea, <a href="/A182008/b182008.txt">Table of n, a(n) for n = 1..10000</a>

%H 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.

%t Table[Ceiling[Sqrt[2 n Log[2]]], {n, 100}] (* _Vincenzo Librandi_, Aug 23 2015 *)

%o (Magma) [Ceiling(Sqrt(2*n*Log(2))): n in [1..100]]; // _Vincenzo Librandi_, Aug 23 2015

%o (PARI) a(n) = { ceil(sqrt(2*n*log(2))) };

%o apply(n->a(n), vector(88, i, i)) \\ _Gheorghe Coserea_, Aug 23 2015

%Y Approximates A033810.

%K nonn

%O 1,1

%A _David Brink_, Apr 06 2012