# [seqfan] Re: A269526, an infinite Sudoku-type array

israel at math.ubc.ca israel at math.ubc.ca
Fri Jul 1 01:54:49 CEST 2016

```A somewhat less trivial sequence with this property
(not yet in OEIS) is a(n) = n/8 if A007814(n) == 3 mod 4, else a(n) = 2n.

2, 4, 6, 8, 10, 12, 14, 1, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40,
42, 44, 46, 3, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78,
5, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 7,
114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142,
9, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172,
174, 11, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200

I think I'll submit it.

Cheers,
Robert

On Jun 30 2016, israel at math.ubc.ca wrote:

>Of course there are permutations of order 4. For example, a(4k)=4k-3,
>otherwise a(n)=n+1:
>
>2, 3, 4, 1, 6, 7, 8, 5, 10, 11, 12, 9, 14, 15, 16, 13, 18, 19, 20, 17, 22,
>23, 24, 21, 26, 27, 28, 25, 30, 31
>
>Hmm, that seems to match a shift of A109680 without the first term, at
>least for the given Data.
>
>Cheers,
>Robert
>
>
>On Jun 30 2016, Paul D Hanna wrote:
>
>>Nice observation, Don.
>>
>> I think it is interesting that, if a(n) = A065189(n), then the following
>> 'almost' holds:
>>
>>     a(a(a(a(n)))) = n
>>
>> That causes me to wonder if someone knows of a non-trivial example of
>> such a sequence.
>>
>> Question: Is there a non-trivial permutation of the natural numbers a(n)
>> such that a(a(n)) results in a self-inverse permutation?
>>
>>Surely there are several examples of such a sequence in the OEIS ...
>>
>>---------- Original Message ----------
>>From: Don Reble <djr at nk.ca>
>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>Subject: [seqfan] Re: A269526, an infinite Sudoku-type array
>>Date: Thu, 30 Jun 2016 00:10:13 -0600
>>
>>
>>> There are a lot of other related sequences, for example, in row n, where
>>> does 1 appear?
>>