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Sequence and the greatest odd divisor

Source: Problem 3, Polish NO 1993

October 6, 2005

number theory solvednumber theory

Problem Statement

Denote

g(k)

as the greatest odd divisor of

k

. Put

f(k) = \dfrac{k}{2} + \dfrac{k}{g(k)}

for

k

even, and

2^{(k+1)/2}

for

k

odd. Define the sequence

x_1, x_2, x_3, ...

by

x_1 = 1

,

x_{n+1} = f(x_n)

. Find

n

such that

x_n = 800

.

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