# [seqfan] Re: SeqFan Digest, Vol 42, Issue 7

Neil Sloane njasloane at gmail.com
Tue Mar 20 19:57:41 CET 2012

This seems like an excellent idea!

Rather than putting this information into the %O line, however,
another possibility, requiring fewer changes to the existing set-up,
might be to put the information into the %Y (cross-references) section,
by adding a line saying
%Y A000040 Indexed by A000027
or
%Y A007318 Indexed by A003056, A002262
Neil

On Tue, Mar 20, 2012 at 2:42 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:

> On Sun, Mar 18, 2012 at 9:23 PM,  <seqfan-request at list.seqfan.eu> wrote:
>
> My proposal is to modify the current %O entry to specify of one or more
> index sequences.  For instance, the %O line of A000040 (the prime
> numbers) would become:
>
> %O A000040 A000027
>
> This says that A000040 is indexed on A000027 (the nonnegative integers).
> Thus we have
>
> n    = A000027   1   2   3   4   5   6   7 ...
> a(n) = A000040   2   3   5   7  11  13  17 ...
>
> This is much prettier and more general that the current scheme, which
> allows only consecutive indices.  For instance, we can now express that
> A003649 is indexed on the squarefrees by stating:
>
> %O A003649 A005117
>
> For tables, we give a %O line with two index sequences.  For instance:
>
> %O A007318 A003056 A002262
>
> gives
>
> x      = A003056   0   1   1   2   2   2   3 ...
> y      = A002262   0   0   1   0   1   2   0 ...
> a(x,y) = A007318   1   1   1   1   2   1   1 ...
>
> This approach allows us to build free-form tables of any dimension.  It
> transforms the integer sequence database to an integer function database,
> which is really what we want if we are including tables.
>
>

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