# sequence information service

Antti Karttunen karttu at megabaud.fi
Tue Feb 5 14:54:44 CET 2002

```
Marc LeBrun wrote:

>  >=Michael Somos
>  > ...it is not immediately obvious that A005775(10)=3858 because that
>  > depends on the origin which is listed on another line '%O A005775 3,2'.
>
> Good point.  However I find the one-value-per-line format too verbose.  How
> about if it returned the range of indices for each line?  For example,
>
> A005775(3:15) 1,4,14,45,140,427,1288,3858,11505,34210,101530,300950,891345
>
> Also, in a related vein, I've been fretting over the initial index issue
> with the superseeker transforms.  Some transforms, like differences, are
> highly index-independent, but many others, such as Mobius, can be
> exquisitely sensitive to the "registration".  What happens with initial
> zero-padding in transforms, both for the EIS entries and the lookup sequence?

The problem here is that OEIS is a database of "integer sequences", while
sometimes one actually seeks N -> N or N -> Z functions, and there's
many-to-one mapping from the latter to former (depending where
you set the offset).

For example, I have been thinking about creating a few entries exemplifying
primitively and not primitively recursive functions, using
David Boozer's nice bijection and table given at:
http://www.its.caltech.edu/~boozer/symbols/pr.html

So there would be a table with all-zero sequence (A000004)
as its top row, then the next row is successor function a(n) = n+1,
getting values 1,2,3,4,5,6,7,8,9,... i.e. A000027 but
with offset 0 instead of 1, then the identity function, i.e. A001477,
then as the third row the "monus" function (in Dave's p.r. notation as R 0 p2_1)
which gives 0,0,1,2,3,4,5,6,7,8,9, i.e. a(0) = 0, a(n) = n-1 otherwise.
(I am sorry, but the terms do not match anything in the table).

I have also another name for this function: "Unary Shift Right"
or "Unary Right Shift".
I.e.

write n out in unary, then
shift one of the (s)ticks right,
and count what was left.

What do you think Neil, is this too much for OEIS?