[seqfan] Re: Is there a correct way to submit a family of sequences?

[M. F. Hasler]

On Tue, Nov 30, 2021 at 8:14 AM Oliver Seet  wrote:

> (...). Since the range of sequences generated is the
> same as the number of possible bases ( infinite ) I realize that I can't
> just submit all of the sequences. Is there a way to submit a family of

sequences or do I just have to pick a few that are interesting from it?
>

The "canonical" way to submit infinite families of sequences is as an
infinite square array,
where row m would list the m-th member of the family.
(Such square arrays are entered by falling antidiagonals, consider
oeis.org/A27/table in case you forget;
offset would be 2 if it starts with row (=base) 2, in your case.)

But of course you may submit a few representative sequences (base 16, 8, 2
if it makes sense(?)) separately ;
you xref'd A068505 = the base 10 variant, already in OEIS.
Unless I'm wrong, the base 8 (and other bases B < 10) variant is obtained
from the base 10 variant
by deleting the terms corresponding to numbers which have (decimal) digits
>= 8.
(i.e., if a(n) = A068505(n), then the base 8 version would be  a(0..7),
a(10..17), a(20..27) etc.
The base-16 variant b(n) should have the base-10 variant as subsequence
b(0..9), b(16..25), b(32..41), etc)
So I suspect that the infinite square array which contains all of these
sequences might not look that interesting, but why not -- to have
infinitely many sequences within a single one makes it relatively "cheap".)

(PARI) row(b,N=30)=vector(N,n, fromdigits(N=digits(n,b),vecmax(N)+1))
row(2) = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]
/* (obviously not to submit as separate seq.) */
row(3) = [1, 2, 2, 3, 5, 6, 7, 8, 4, 5, 11, 6, 7, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 8, 9, 29, 10]
row(8) = [1, 2, 3, 4, 5, 6, 7, 2, 3, 5, 7, 9, 11, 13, 15, 6, 7, 8, 11, 14,
17, 20, 23, 12, 13, 14, 15, 19, 23, 27]
/* as expected, A068505 without n = 8,9, 18,19, 28,29 ... */

- Maximilian


> While the case for base 10 has been submitted by someone else already, I
> would like to submit bases 8,16 and 60.
>
> I searched for the sequences and did find a member of the family.  A068505
> <https://oeis.org/A068505>
>
(...)
In base 16 the sequence represented in decimal begins with:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,2,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,6,7,8,11,14,17,20,23,26,29,32,35,38,41,44,47,12,13,14,15,19,23,27,31,35,39,43,47,51,55,59,63,20,21,22,23,24,29,34,39,44,49,54,59,64,69,74,79,30,...