An Odd-Valued Recurrence

★ 4/10Geometric Progression number theory Recursion sequences

Problem

A sequence $\{a_n\}$ is defined for $n \in \mathbb{N}^*$ by

a_n = \begin{cases} n, & n \text{ odd}, \\ a_{n/2}, & n \text{ even}, \end{cases}

so every term of the sequence is odd.

1. Find $a_{24} + a_{25}$ . 2. Each odd number appears in the sequence infinitely often. At which position does the number $5$ appear for the $8$ th time?

Answer

Solution

Difficulty	4/10
Topics	Geometric Progression, number theory, Recursion, sequences

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