# Can you find the pattern?

beamthegreat
I believe I have created an integer sequence that is truly unique. I would appreciate it if someone could try to solve this.

Here is the first 89 integers of this sequence: 1,0,1,1,1,1,1,2,2,3,0,1,0,3,0,3,0,5,2,3,1,0,1,3,1,3,1,6,4,9,4,5,4,9,4,9,4,13,8,5,1,0,1,5,1,5,1,10,6,13,6,7,6,13,6,13,6,19,12,7,1,0,1,7,1,7,1,14,8,25,16,17,16,25,16,25,16,33,24,18,10,9,10,18,10,18,10,27,19

Here is a graph of this sequence:

Haborix
What makes an integer sequence unique?

Mentor
I believe I have created an integer sequence that is truly unique. I would appreciate it if someone could try to solve this.

Here is the first 89 integers of this sequence: 1,0,1,1,1,1,1,2,2,3,0,1,0,3,0,3,0,5,2,3,1,0,1,3,1,3,1,6,4,9,4,5,4,9,4,9,4,13,8,5,1,0,1,5,1,5,1,10,6,13,6,7,6,13,6,13,6,19,12,7,1,0,1,7,1,7,1,14,8,25,16,17,16,25,16,25,16,33,24,18,10,9,10,18,10,18,10,27,19
What is the prize?

I can create a random sequence as well, so what's the point? Are you saying that you used some generator function that if we're smart enough we should be able to figure it out? Can you at least bound the problem? How many terms did you use in your generator function? If you used 20 terms, it will be a waste of my time, no?

Gold Member
2022 Award
So, you are not interested in finding out if your pattern is unique to your particular creation algorithm, right? If the pattern is NOT unique, you don't care, you just want to see if we can identify the pattern.

Homework Helper
Gold Member
Using the first 10
https://oeis.org/search?q=1,0,1,1,1,1,1,2,2,3&sort=&language=english&go=Search

Hmmm..
let me come up with another integer sequence that is truly unique
7 15 22 36 64 13 6 40 41 45 52 9 5 7 61 63 69 18 18 30 35 52 56 5 4 5 6 28 67 10 37 39 55 63 69 23 18 27 33 39 44 8
...this one is finite... but could become countably infinite...
building the sequence by prepending, rather than appending.
Generating this integer sequence might also be of value.

Here's a search on a subset https://www.google.com/search?q=6+40+41+45+52+9

Gold Member
Um, what's the point here? It doesn't match the 11th term. Am I missing something?

Homework Helper
Gold Member
Um, what's the point here? It doesn't match the 11th term. Am I missing something?
The On-Line Encyclopedia of Integer Sequences (or OEIS) a place where one can search for such sequences.
It might even provide a clue to how such sequences arise
... especially since the OP didn't provide much of a clue.

If the OP's sequence is "of general interest", it can be contributed.

Gold Member
Here is the first 89 integers of this sequence: 1,0,1,1,1,1,1,2,2,3,0,1,0,3,0,3,0,5,2,3,1,0,1,3,1,3,1,6,4,9,4,5,4,9,4,9,4,13,8,5,1,0,1,5,1,5,1,10,6,13,6,7,6,13,6,13,6,19,12,7,1,0,1,7,1,7,1,14,8,25,16,17,16,25,16,25,16,33,24,18,10,9,10,18,10,18,10,27,19

Here is a graph of this sequence:
I do not think so.

For example, your sequence contains a whole pile of zeroes, and yet nary-a-one appears in your graph. There's a big problem with the resolution.

Last edited:
phinds and robphy
Staff Emeritus