[seqfan] Re: Can we write this definition in a better way?

[Tw Mike]

Odd indexes elements:
a[4 * 4^ n + 1] = 4 * n + 1

Should be:
a[(2 * n + 2)^2 + 1] = 4 * n + 1

Mike,

2019-10-02 19:51 GMT+08:00, Tw Mike <mt.kongtong at gmail.com>:
> Odd indexes elements:
> a[4 * 4^ n + 1] = 4 * n + 1
>
> 5, 2, 4, 3
> 9, 2, 4, 3, 8, 7
> 13, 2, 4, 3, 8, 7, 12, 11
> ...
>
> Even indexes elements:
> a[4 * (n^2 + 4 * n + 5)] = 4 * n + 8
> 12, 5, 4, 9
> 16, 5, 4, 9, 8, 13
> 20, 5, 4, 9, 8, 13, 12, 17
> ...
>
> Hope this helps
>
> Mike,
>
> 2019-09-30 9:59 GMT+08:00, Ali Sada via SeqFan <seqfan at list.seqfan.eu>:
>>  Dear Dr.  Hasler,
>> Thank you very much! This table might look trivial to you, but it
>> definitely
>> looks beautiful to me. I would really appreciate it if you could add it
>> to
>> the sequence when it gets published.
>> Best,
>> Ali
>>
>>     On Sunday, September 29, 2019, 6:38:59 PM EDT, M. F. Hasler
>> <seqfan at hasler.fr> wrote:
>>
>>  Dear Ali & SeqFans:I also found this sequence interesting, but I think
>> there is a pattern making the sequence somewhat trivial to compute.If we
>> consider the sequence as a table of rows of length = max(2n-1,1),
>> n=0,1...
>> then, starting with row n=5 : (i.e., starting with a(18)=1)- all rows
>> start
>> with 1, and there are no other 1's,- the even rows are of the form
>>  (1, 2n-4, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, ...,
>> 2,3,
>> 2n-3)  where the terms between (1,2n-4) and (2,3, 2n-3) are [ (2k+1, 2k),
>> k=1..2n-3 ]- the odd rows are of the form  (1, 2, 2n-2, 4, 5, 3, 4, 8, 9,
>> 7,
>> 8, 12, 13, 11, 12, 16, 17, 15, 16,..., 3, 2n-4)  where the terms between
>> 2n-2 and (3, 2n-4) follow the simple pattern [ (4k, 4k+1, 4k-1, 4k),
>> k=1..2n-6 ].
>> A327759 = [1, /* row n=0 */
>> 2,  /* row n=1, from here on, length=2n-1 */2, 3, 1,  /* n=2 */2, 1, 4,
>> 5,
>> 1,  /* n=3 */2, 4, 1, 5, 1, 2, 5, /* n=4 */1, 2, 8, 4, 5, 3, 4, 3, 6, /*
>> n=5
>> */1, 8, 3, 2, 5, 4, 7, 6, 2, 3, 9,  /* n=6 */1, 2, 12, 4, 5, 3, 4, 8, 9,
>> 7,
>> 8, 3, 10, /* n=7*/1, 12, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 2, 3, 13, /* n=8
>> */
>> 1, 2, 16, 4, 5, 3, 4, 8, 9, 7, 8, 12, 13, 11, 12, 3, 14,  /* n=9 */1, 16,
>> 3,
>> 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 2, 3, 17,  /* n=10 */1, 2,
>> 20,
>> 4, 5, 3, 4, 8, 9, 7, 8, 12, 13, 11, 12, 16, 17, 15, 16, 3, 18,  /* n=11
>> */1,
>> 20, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 2, 3,
>> 21,  /* n=12 */1, 2, 24, 4, 5, 3, 4, 8, 9, 7, 8, 12, 13, 11, 12, 16, 17,
>> 15,
>> 16, 20, 21, 19, 20, 3, 22,  /* n=13 */1, 24, 3, 2, 5, 4, 7, 6, 9, 8, 11,
>> 10,
>> 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 2, 3, 25,   /* n=14 */1,
>> 2,
>> 28, 4, 5, 3, 4, 8, 9, 7, 8, 12, 13, 11, 12, 16, 17, 15, 16, 20, 21, 19,
>> 20,
>> 24, 25, 23, 24, 3, 26,   /* n=15 */1, 28, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10,
>> 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 2, 3, 29,
>> /* n=16 */1, 2, 32, 4, 5, 3, 4, 8, 9, 7, 8, 12, 13, 11, 12, 16, 17, 15,
>> 16,
>> 20, 21, 19, 20, 24, 25, 23, 24, 28, 29, 27, 28, 3, 30,   /* n=17 */1, 32,
>> 3,
>> 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23,
>> 22,
>> 25, 24, 27, 26, 29, 28, 31, 30, 2, 3, 33,   /* n=18 */1, 2, 36, 4, 5, 3,
>> 4,
>> 8, 9, 7, 8, 12, 13, 11, 12, 16, 17, 15, 16, 20, 21, 19, 20, 24, 25, 23,
>> 24,
>> 28, 29, 27, 28, 32, 33, 31, 32, 3, 34,   /* n=19 */...]This may be a bit
>> tedious but straightforward to prove.
>>
>> I also suggest that the simpler triangle mentioned by Chris,with rows of
>> length 2n, going (1, 3,3, 5,5, ..., 1, 2n-1, 2n), could also be
>> submitted. -
>> Maximilian
>>
>>
>>>> Hi Everyone,
>>>>
>>>> Please see the sequence below. I just want to see if thereis there is a
>>>> better way to write its definition. OEIS editors usually strugglewith
>>>> my
>>>> language, and I would really appreciate it if you could help me
>>>> maketheir
>>>> job easier.
>>>>
>>>> The sequence:
>>>>
>>>> 1 ,2 ,2 ,3 ,1 ,2 ,1 ,4 ,5 ,1 ,2 ,4 ,1 ,5 ,1 ,2 ,5 ,1 ,2 ,8 ,4,5 ,3 ,4
>>>> ,3
>>>> ,6 ,1 ,8 ,3 ,2 ,5 ,4 ,7 ,6 ,2 ,3 ,9 ,1 ,2 ,12 ,4 ,5 ,3 ,4 ,8 ,9 ,7,8 ,3
>>>> ,10
>>>> ,1 ,12 ,3 ,2 ,5 ,4 ,7 ,6 ,9 ,8 ,11 ,10 ,2 ,3 ,13 ,1 ,2 ,16 ,4 ,5 ,3
>>>> ,4,8
>>>> ,9
>>>> ,7 ,8 ,12 ,13 ,11 ,12 ,3 ,14 ,1 ,16 ,3 ,2 ,5 ,4 ,7 ,6 ,9 ,8 ,11 ,10 ,13
>>>> ,12,15 ,14 ,2 ,3,……
>>>>
>>>> The definition:
>>>> a(1)=1; a(2)=2;
>>>> a(n)=n-m1, if a(n-1) is odd;
>>>> a(n)=n-m2, if a(n-1) is even;
>>>> m1 is the most recent position of the largest term up toa(n-1);
>>>> m2 is the most recent position of the second largest term upto a(n-1)
>>
>>
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>