turkey-yks 2013 Q33

turkey-yks · Other · lys1-math Number Theory Properties of Integer Sequences and Digit Analysis

For a positive integer n, the greatest odd divisor of n is denoted by $\overline{n}$. The terms of the sequence $( a _ { n } )$ are defined for $n = 1,2 , \ldots$ as
$$a _ { n } = \begin{cases} n + 1 , & \text{if } n \equiv 1 ( \bmod 4 ) \\ n - 1 , & \text{if } n \equiv 3 ( \bmod 4 ) \end{cases}$$
Given this, what is the difference $a _ { 18 } - a _ { 12 }$?
A) 2
B) 4
C) 6
D) 8
E) 10

For a positive integer n, the greatest odd divisor of n is denoted by $\overline{n}$.\\
The terms of the sequence $( a _ { n } )$ are defined for $n = 1,2 , \ldots$ as

$$a _ { n } = \begin{cases} n + 1 , & \text{if } n \equiv 1 ( \bmod 4 ) \\ n - 1 , & \text{if } n \equiv 3 ( \bmod 4 ) \end{cases}$$

Given this, what is the difference $a _ { 18 } - a _ { 12 }$?\\
A) 2\\
B) 4\\
C) 6\\
D) 8\\
E) 10

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