[seqfan] Re: Move, add, delete, repeat

[Ali Sada]

 Hi Brad,
This is amazing and really encouraging! Thank you! I tried to find a link between the two sequences, but to be honest, I have a severe comprehension problem and I couldn't fully understand A004641. 

On the definition issue, I gave ChatGPT the  VBA program I used to find the terms of this sequence (below) and I asked it for a definition. This is what I got 

"S(1) = 1, For i = 2 to n: S(i) = S(i) + S(i + S(i)). Shiftthe remaining values in the sequence to the left, starting from position i +S(i)"

And here is the program I used 
n = 500
For i = 1 To n
Cells(1, i) = i
Next i

For i = 1 To n
k1 = Cells(1, i)
k2 = i + Cells(1, i)

Cells(1, i) = Cells(1, i) + Cells(1, k2)
For j = k2 To n
Cells(1, n + i) = n + i
Cells(1, j) = Cells(1, j + 1)
Next j
Next i
Best,
Ali 






Best,
Ali 

    On Saturday, May 27, 2023 at 07:34:04 AM GMT+1, brad klee via SeqFan <seqfan at list.seqfan.eu> wrote:  
 
 Could the first differences be related to A004641? 

I tried with Mathematica and matched all your terms: 

Accumulate[Prepend[2 (Nest[Flatten[
        # /. {0 -> {1, 0}, 1 -> {1, 0, 0}}
        ] &, {1}, 5] + 2), 3]] 

--Brad

------- Original Message -------
On Friday, May 26th, 2023 at 10:18 PM, Ali Sada via SeqFan 
> 3, 9, 13, 17, 23, 27, 33, 37, 43, 47, 51, 57, 61, 67, 71, 75,81, 85, 91, 95, 99, 105, 109, 115, 119, 125, 129, 133, 139, 143, 149, 153, 157,163, 167, 173, 177, 183, 187, 191, 197, 201, 207, 211, 215, 221, 225, 231, 235,241, 245, 249, 255, 259, 265, 269, 273, 279, 283, 289, 293, 297, 303, 307, 313,317, 323, 327, 331, 337, 341, 347, 351, 355, 361, 365, 371, 375, 381
> 
> 
> I need some help with the exact definition of this sequence.

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