

A182008


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


5



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, 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, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 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 on a set of integers n with density (3+2 log 2)/6 = 0.731...


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.


MATHEMATICA

Table[Ceiling[Sqrt[2 n Log[2]]], {n, 100}] (* Vincenzo Librandi, Aug 23 2015 *)


PROG

(MAGMA) [Ceiling(Sqrt(2*n*Log(2))): n in [1..100]]; // Vincenzo Librandi, Aug 23 2015
(PARI) a(n) = { ceil(sqrt(2*n*log(2))) };
apply(n>a(n), vector(88, i, i)) \\ Gheorghe Coserea, Aug 23 2015


CROSSREFS

Approximates A033810.
Sequence in context: A061555 A146323 A071626 * A106457 A103128 A156080
Adjacent sequences: A182005 A182006 A182007 * A182009 A182010 A182011


KEYWORD

nonn


AUTHOR

David Brink, Apr 06 2012


STATUS

approved



