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wintersolstice

Real Member

Registered: 2009-06-06

Posts: 128

A possibly interesting sequence

This is actually one of 3 things (main things) I've been studying/investigating recently, (maybe I'll post the other 2 at a later date)

It's a sequence I created and I wanted to submit it to the OEIS (Online Encyclopaedia if Integer Sequences) the only problem is, to submit anything you need to register an account and unfortunately, since I don't have any official credentials (I don't work in fields of maths or anything and don't know any who is a member) I can't register. (btw I did search the OEIS for my sequence and far as I know it wasn't there) so I thought I'd try sharing it here. to get some opinions but also to get help studying and generating it. I don't know anything about computer programming, my only tool is an Excel Spreadsheet which is limited to what it can do and it can't offer much help to generate the sequence (I think I generated about 40 terms by brute force, but can't find where I saved them, so I'll only be able to post a few terms.

Any to describe the sequence I need to define a "super-block"

a super-block, is a set of consecutive terms with the following property:

you have a repeated block that appears multiple times in the "super-block" which is seperated by gaps of equal length. Below is a few examples

1)

In this case the repeated block is

and it has a gap of length 3.  which are:

2)

the repeated block is

and the gaps are

now there are two values

gap count: the number of gaps (1 less than the number repeated blocks)
gap length: how many terms (not digits) are in each gap

the gaps don't have to be the same, only the same length

the repeated blocks have to be identical (same terms, same order, same abundance)

a super block is illegal if its gap count is greater than it gap length

to explain consider

repeated block is

it has 1 gap of length 0 (yes that's still considered a gap)

so it's illegal

same repeated block, this now has 1 gap of length 1 so it's allowed

same repeated block, this now has 2 gaps of length 1 so it's  not allowed

also the super block can start anywhere in the sequence

now to the sequence

you start by asking "can I put 1" if so do, if not try 2 then 3 etc

so

(no problems

 

repeating block 

 

1 gap of length 0 (this will happen if two consecutive terms are the same

so

no problem

repeating block 

 

1 gap of length 1 no problem

we can't use 1 (because of above and 2 would be another 1 gap of length 0 repeated block of

so

next we might try

 

2 gaps of length 1 so not allowed so

and so on

but that's a block of

Last edited by wintersolstice (2021-08-27 08:45:08)

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