[seqfan] A sequence and a few questions
Ali Sada
pemd70 at yahoo.com
Wed Jul 5 14:51:49 CEST 2023
Hi everyone,
Start with a list of positive integers 1,2,3,4… Take each number in the list (m) in turn and repeat it m times. Place the repeated numbers in non-consecutive locations to the right of m and amend the list accordingly.
We start with
1,2,3,4,5,6,7,8,9,10…
We repeat the 1 one time and put it after 2.
1,2,1,3,4,5,6,7,8…
We repeat the 2 twice and place the new “copies” after the second 1 and the first 3
1,2,1,2,3,2,4,5,6,7,8….
We repeat the 3 three times and place the new repeats after the first 3 such that they are not in consecutive positions
1,2,1,2,3,2,3,4,3,5,3,6,7,8…
And so on. We get:
1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 3, 5, 4, 5, 6, 5, 6, 4, 6, 5, 6, 7, 6, 7, 8, 7, 8, 6, 8, 7, 8…
1. Is this sequence suitable for the OEIS?
2. Is the definition above accurate?
3. Can we find a general formula?
4. If we tweak the definition a little bit: “Start with a list of positive integers 1,2,3,4… Take each number in the list (m) in turn and repeat it m times. Place the repeated numbers in non-consecutive locations such that the first appearance of m occurs at n = m.
1,2,3,4,5,6,7,8…
1,2,1,3,4,5,6,7…
1,2,1,3,2,4,5,6,7…
1,2,3,1,3,2,3,4,3,5,6,7…
1,2,3,4,1,4,3,4,2,4,3,4,5…
Gradually we will have 1,2,3,4,5,6,7…
Is this sequence equal to A000027 (regardless of the fact that there are countless numbers that are supposed to appear “later”)?
Best,
Ali
More information about the SeqFan
mailing list