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,
completely out of your sight,
and count what was left.
What do you think Neil, is this too much for OEIS?
With gradually lessening remorse,
Antti
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