[seqfan] Re: The Annoyance Sequence

[Yifan Xie]

First of all, your sequence looks wrong: At the first turn, 2 is annoyed; At the second turn, 3 is not annoyed.
Maybe you can change the definition to:
For the nth turn, find the smallest number x which all the numbers behind it's position is not changed. a(x-1) numbers are annoyed.
Example:
1->
(first turn)1,3,4,2->
(second turn)1,3,4,2,6,7,8,9,10,5->1,3,4,2,7,8,9,10,5,11,6->
(third turn) 6 numbers starting from 12 are annoyed.

Best regards,
Yifan Xie

(xieyifan4013 at 163.com)




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xieyifan4013 at 163.com
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Email:xieyifan4013 at 163.com
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---- Replied Message ----
| From | Ali Sada via SeqFan<seqfan at list.seqfan.eu> |
| Date | 07/16/2023 09:34 |
| To | Sequence Fanatics Discussion List<seqfan at list.seqfan.eu> |
| Cc | Ali Sada<pemd70 at yahoo.com> |
| Subject | [seqfan] The Annoyance Sequence |
Hi everyone,
We start with the list of positive integers 1,2,3,4,....When it turn comes, a(n) can annoy a(n) numbers and force them to jump to the right and insert themselves. When annoyed, the number m can jump m steps.
We start with a(1) =1. The 1 can annoy only 1 number, 2. The 2 jumps 2 steps and the list becomes 1,3,4,2,5,6,7,8,9...Now, a(2) = 3. It annoys 3 numbers and force them to jump
First, the 4 jumps 4 steps 1,3,2,5,6,7,4,8,9Then the 2 jumps 2 steps 1,3,5,6,2,7,4,8,9Finally, the 5 jumps 5 steps 1,3,6,2,7,4,8,5,9At this stage, 3 finished its annoyance and a(3) = 6, which in turn annoys 6 numbers and so on.
The resulted sequence is
1, 3, 6, 2, 10, 9, 5, 8, 22, 4, 13, 15, 20, 29, 7, 12, 18, 32,59, 50, 19, 31, 14, 81, 16, 90, 17, 25, 78, 83, 21, 46, 65, 23, 41, 71, 64, 36,53, 47, 58, 44, 35, 76, 62, 43, 88, 49, 123, 116, 27, 111, 40, 11, 69, 30, 79, 102,24, 60, 159, 73, 248, 72, 55, 185, 45, 101, 38, 95, 141
I would really appreciate any help defining this sequence, if it were suitable for the OEIS. Note: Maybe the VBA/Excel program below explains the sequence better

Sub Annoyance()
For i = 1 To 1000
    Cells(1, i) = i
    Next iFor i1 = 1 To 71     k1 = Cells(1, i1)
     For i2 = i1 + 1 To i1 + k1
         k2 = Cells(1, i1 + 1)
         For i3 = i1 + 1 To i1 + k2
             Cells(1, i3) = Cells(1, i3 + 1)
         Next i3
     Cells(1, i1 + k2 + 1) = k2
     Next i2
Next i1
End Sub
Best,
Ali



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