Observe... :-)

Number Theory Level 2

Given the following two sequences: $1,2,4,6,10,12, A,...$

$4,8,32,128,2048,8192, B...$

$A$ and $B$ are the subsequent terms in the corresponding series. If $B =kA,$ find $k$ .

The answer is 8192.

1 solution

A Former Brilliant Member
Jun 12, 2014

The first sequence is the sequence of p-1 where p is a prime number.The second sequence is $2^p$ , where again p is a prime number. Therefore, $k=\frac {B}{A}=\frac{2^{17}}{16}=\frac{2^{17}}{2^{4}}=2^{13}=\boxed {8192}$

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A Former Brilliant Member - 6 years, 12 months ago

Observe... :-)

The answer is 8192.

1 solution

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