Multiplibonacci #1

Algebra Level pending

A number in the Multiplibonacci sequence is equal to the product of the previous two numbers in the sequence. The first number in the sequence is 1, and the second number in the sequence is $x$ (for example, ${ _{ 2 }{ M } }=1,2,2,4,8,32,256...$ ).

The Multiplibonacci function takes in two numbers - $x$ and $n$ - and gives an output, $y$ . $x$ is the second number in the sequence, and the function is defined as the $n$ th number in that sequence (for example, ${ _{ 2 }{ M }_{ 6 } }=32$ ).

What is the value of ${ _{ 208 }{ M }_{ 5 } }$ ? (Think about what that 5 really means!)

This problem is part of the Multiplibonacci set.

The answer is 8998912.

1 solution

Louis Ullman
May 17, 2018

Let's look at the first few terms of ${ _{ 208 }{ M } }$ so we can find ${ _{ 208 }{ M }_{ 5 } }$ :

${ _{ 208 }{ M }_{ 1 } }=1\\ { _{ 208 }{ M }_{ 2 } }=208\\ { _{ 208 }{ M }_{ 3 } }=208\cdot 1=208\\ { _{ 208 }{ M }_{ 4 } }=208\cdot 208={ 208 }^{ 2 }\\ { _{ 208 }{ M }_{ 5 } }={ 208 }^{ 2 }\cdot 208={ 208 }^{ 3 }=8998912$

So ${ _{ 208 }{ M }_{ 5 } }$ = $\boxed { 8998912 }$ .

Multiplibonacci #1

The answer is 8998912.

1 solution

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