Maths Question: Is it possible to find the nth term for this sequence?

By well-wisher

Wed, 07 Mar 2018
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2 comments
 

I was watching a Maths video on YouTube recently that explained how you work out the nth term in a sequence and a question occurred to me.
Here is a type of sequence:
Pick first number
and add the number of letters in that number to it;
add the number of letters in your resulting number;
add the number of letters in your resulting number etcetera
For example:
Lets pick 4 as a first number.
Four has 4 letters in it (F-O-U-R) so add  4 to 4
and you get eight which has 5 letters (E-I-G-H-T) so add 5 to 8
and you get thirteen which has eight letters so add 8 to 13
which gives you 21 etcetera
My question is: Is it possible to find the nth term for this kind of sequence?

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Comments

Submitted by Ed Crane on

 

 

Submitted by well-wisher on

I was really hoping for a more detailed answer. I would have thought the sequence would be too irregular.

And you have to realize that the number of letters you add would keep growing irregularly and whatever nth term you work out would have to be correct up to the highest number with a name.

You see, early on in the sequence I'd only have to add numbers with a few letters like nine (with only 4 letters).

But later on in the sequence I'd have to add the letters in long numbers like Five million, nineteen thousand, eight hundred and seventy two.

Then, after it has passed all the quadrillions, hexillions and nonillions then you get to the duodecillions and the septendecillions; the octaquadragintillions (10 to the power of 147); trecennovemquinquagintillions (10 to the power of 1080) and tremilliatrecennovemvigintillions (10 to the power of 9990) etcetera.

 

 

 

 

Oh look, a link. I wonder where it leads.

JoHn