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integers in the form n = 2^b(2c+1), odd parts and sequence

Source: Brazilian Mathematical Olympiad 1982 P2

July 27, 2018
number theorySequencepositive integer

Problem Statement

Any positive integer nn can be written in the form n=2b(2c+1)n = 2^b(2c+1). We call 2c+12c+1 the odd part of nn. Given an odd integer n>0n > 0, define the sequence a0,a1,a2,... a_0, a_1, a_2, ... as follows: a0=2n−1,ak+1a_0 = 2^n-1, a_{k+1} is the odd part of 3ak+13a_k+1. Find ana_n.
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