

A182009


a(n) = ceiling(sqrt(2n*log(2))+(32*log(2))/6).


5



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, 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, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET

1,1


COMMENTS

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.


LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..10000
D. Brink, A (probably) exact solution to the Birthday Problem, Ramanujan Journal, 2012, pp 223238.


MAPLE

seq(ceil((2*n*log(2))^(1/2) + (32*log(2))/6), n=1..1000); # Robert Israel, Aug 23 2015


MATHEMATICA

Table[Ceiling[Sqrt[2 n Log[2] + (3  2 Log[2])/6]], {n, 82}] (* Michael De Vlieger, Aug 24 2015 *)


PROG

(PARI)
a(n) = { ceil((2*n*log(2))^(1/2) + (32*log(2))/6) };
apply(n>a(n), vector(84, i, i)) \\ Gheorghe Coserea, Aug 23 2015


CROSSREFS

Approximates A033810.
Sequence in context: A036042 A162988 A143824 * A034463 A259899 A071996
Adjacent sequences: A182006 A182007 A182008 * A182010 A182011 A182012


KEYWORD

nonn


AUTHOR

David Brink, Apr 06 2012


STATUS

approved



