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

[David Sycamore]


Hi Ali, try this:

Start with list L_1 = 1,2,3,4,….the +ve integers

Calculate a(n) from L_n, then modify L_n to get L_(n+1), from which a(n+1) is found, and so on. Use the following rules: 

a(n) = L_n(1) + L_n(L_n(1) + 1). 

Delete L_n(1) and L_n(L_n(1) + 1) from L_n, and adjust indices to obtain L_(n+1).

Example: to compute a(5) then a(6):
L_5 = 7,8,10,11,13,14,15,16,…
a(5) = L_5(1) + L_5(L_5(1) + 1) = 7 + 16 = 23
then L_6 = 8,10,11,13,14,15,17,18,19,20,..
a(6) = 8 + L_6(9) = 8 + 19 = 27

and so on…


Best regards
David Sycamore.


> On 27 May 2023, at 06:04, Ali Sada via SeqFan <seqfan at list.seqfan.eu> wrote:
> Hi everyone,
> We have a list of positive integers. We start at 1 and move 1 step to reach 2. We add 1+2 = 3, which will be a(1). 
> Then, we delete the 2 from the list since we already used it. Now, the second number on the list becomes 3. We move 3 steps and reach 6. a(2) = 3+6 = 9. We delete the 6 from the list. The next remaining number on the list is 4. We move 4 steps and reach 9. a(3)= 4+9 = 13. And so on.
> 
> 
> 
> 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. 
> 
> Best,
> Ali
> 
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