Bit Length

The number of binary bits necessary to represent a number, given explicitly by

			(1)
			(2)

where  is the ceiling function,  is the floor function, and  is lg, the logarithm to base 2. For , 2, ..., the sequence of bit lengths is given by 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, ... (OEIS A036377). The function is given by the Wolfram Language function BitLength[n].

REFERENCES:

Sloane, N. J. A. Sequence A036377 in "The On-Line Encyclopedia of Integer Sequences."