Come up with the general formula for the n-th term of the following sequence:

arithmetic/repeated.integers New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Come up with the general formula for the n-th term of the following
sequence:

1  2  2  3  3  3  4  4  4  4  5  5  5  5  5  6  ...

Show solution

 ceiling( (sqrt( 1 + 8*x) - 1)/2 )

-- Dennis Yelle <dennis@netcom.com>

CORRECT!

-- Naeem Sheikh <nsheikh@itsmail1.hamilton.edu>, who posed the puzzle
   (February 1996)

[ Editor: x is the position n in the sequence. ]