A182008 a(n) = ceiling(sqrt(2*n*log(2))).

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

Offset: 1

Author

David Brink, Apr 06 2012

Keywords

• nonn

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 223-238.

Crossrefs

Approximates A033810.

Programs

Magma

[Ceiling(Sqrt(2*n*Log(2))): n in [1..100]]; // Vincenzo Librandi, Aug 23 2015

Mathematica

Table[Ceiling[Sqrt[2 n Log[2]]], {n, 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