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The exponent of the largest Power of 2 which Divides a given number 
. The values of the ruler
function for 
, 2, ..., are 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, ... (Sloane's A001511).
References
Guy, R. K. ``Cycles and Sequences Containing All Permutations as Subsequences.'' §E22 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 224, 1994.
Sloane, N. J. A. Sequence
A001511/M0127
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.