-2
x=1:1
x=2:2
x=3:3
x=4:6
x=5:9
x=6:15
x=7:25
x=8:39
x=9:63
x=10:99

I've tried using the normal Fibonacci sequence although there were always slight small differences in the numbers.

Thanks!

Jeffplays2005
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Mar 13 '22 at 21:03
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    How does $x=4$ get $6?$ It is unclear what you mean by “custom Fibonacci sequence.” – Thomas Andrews Mar 13 '22 at 21:03
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    This appears to be A114323, $\lceil \sqrt[5] {10^n}\rceil -1 $ – lulu Mar 13 '22 at 21:04
  • I was told this was a custom Fibonacci sequence, therefore x=4 getting 6 is normal – Jeffplays2005 Mar 13 '22 at 21:06
  • @lulu im quite sure that's the answer, could you post it so I can mark it as correct? Much appreciated, thank you so much for answering the question! – Jeffplays2005 Mar 13 '22 at 21:07
  • Well, it is definitely not a “custom Fibonacci sequence” under any definition I know. I suppose it is an integer sequence with exponential growth, but otherwise, I don’t think it has much to do with Fibonacci. There certainly isn’t a linear recursion for the sequence, for example. – Thomas Andrews Mar 13 '22 at 22:20
  • I would expect from a "custom Fibonacci sequence" that we have $a_n=a_{n-1}+a_{n-2}$ for every integer $n\ge 3$. Otherwise the terminology does not really make sense. If we add , for example , the last three numbers, we would have a "custom Tribonacci sequence". – Peter Mar 14 '22 at 09:31
  • Since we cannot find a Fibonacci-pattern, we can only guess what the general term of this sequence is. The answer below gives a so-called "reasonable guess", but we do not know whether the sequence continues this way. – Peter Mar 14 '22 at 10:26
  • Hi, very sorry that I got slightly confused over if this was a Fibonacci pattern, I was given a hint that this may be a Fibonacci sequence, therefore I posted it as one. – Jeffplays2005 Mar 14 '22 at 20:04

1 Answers1

0

This is A114323, $a_n$ is the largest natural number such that $a_n^5$ has $n$ digits.

It can be expressed as $$a_n=\big \lceil \sqrt[5] {10^n}\big \rceil -1$$

lulu
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