DarkDarkly
New member
- Joined
- Jun 19, 2020
- Messages
- 13
So I've been working on generating a sequence of numbers for a while now, and despite having 3 ways to derive this sequence from methods of creating prime numbers, I hadn't figured out what this sequence actually meant. Now by splitting it into 5 rows, one for each single-digit odd number, I've had a much better understanding of the sequence and it's usage. I'll include a photo of the beginning of the sequence, and a download to the spreadsheet if someone wishes to help me solve the last few anomalies, and here I'll explain what I've already learned. (Scroll to the bottom for the part I actually want help with)
Basically the sequence starts on negative one (where the X is in the top left), and continues to count up by 1 until it hits the bottom row, at which point it counts down by 2 and moves one column over to restart at the top. Obviously you will notice all of the Xs, which simply mean the number correlating to it will not result in a prime number. There are a few specific situations that will result in something being an X.
Firsty, ALL multiples of 3 are replaced with Xs.
Second, ALL numbers in the center column (>1) will be Xs.
and Lastly, as far as I have discovered, numbers in a position that counts by the increasing value, 4n, will be and X. starting from -1 and n=0, count by 4n spaces and make that value an X (so -1 becomes an X). Then increase n by 1 and count 4n more spaces (which turns 3 in column 1 into an X, even though rule #1 already did so). Increase n by 1 again and repeat.
The part I need help with is figuring out the remaining rules, like why 25 is mysteriously skipped in the 5th row, 12th column. That one does not follow any of the other rules. Another situation is 26 and 28 in the second row, which are also both skipped. There are many more examples, but too many to include here. I will have a link to a spreadsheet download that contains terms up until 10000ish, which has roughly 5.5k columns. If anyone wants to take a look and maybe help find the last anomalies in the sequence, that would be awesome!
Basically the sequence starts on negative one (where the X is in the top left), and continues to count up by 1 until it hits the bottom row, at which point it counts down by 2 and moves one column over to restart at the top. Obviously you will notice all of the Xs, which simply mean the number correlating to it will not result in a prime number. There are a few specific situations that will result in something being an X.
Firsty, ALL multiples of 3 are replaced with Xs.
Second, ALL numbers in the center column (>1) will be Xs.
and Lastly, as far as I have discovered, numbers in a position that counts by the increasing value, 4n, will be and X. starting from -1 and n=0, count by 4n spaces and make that value an X (so -1 becomes an X). Then increase n by 1 and count 4n more spaces (which turns 3 in column 1 into an X, even though rule #1 already did so). Increase n by 1 again and repeat.
The part I need help with is figuring out the remaining rules, like why 25 is mysteriously skipped in the 5th row, 12th column. That one does not follow any of the other rules. Another situation is 26 and 28 in the second row, which are also both skipped. There are many more examples, but too many to include here. I will have a link to a spreadsheet download that contains terms up until 10000ish, which has roughly 5.5k columns. If anyone wants to take a look and maybe help find the last anomalies in the sequence, that would be awesome!
Last edited by a moderator:
