3

Part of 2005 Korea Junior Math Olympiad

Problems(1)

a_{n+1} =a_n -1 if a_n is even, a_{n+1} =\frac{a_n - 1}{2} if a_n is odd

Source: KJMO 2005 p3

For a positive integer

K

, define a sequence,

\{a_n\}

, as following:

a_1 = K

a_{n+1} =a_n -1

a_n

a_{n+1} =\frac{a_n - 1}{2}

a_n

is odd , for all

n \ge 1

. Find the smallest value of

K

a_{2005}

the first term equal to

0

.

algebraSequencerecurrence relationminimum