[seqfan] Re: seqs whose |differences| are 1,2,3,4,...

Ron Hardin rhhardin at att.net
Thu Mar 11 07:53:49 CET 2010

I didn't follow what the note meant either.

That sequence can't be continued, right; and increasing L (the lookahead) can apparently raise the maximum of 1-1 terms 1..top reached.

I'm less worried about its being lexicographically least than existing.

The method so far however generates only finite sequences.  Is that always true (so there is no 1-1 sequence with the difference property at all) or will some patterns emerge, like  166 56 167 55 168 54 169 53 170 52 171 51 172 50 173 49 174 48 175 47 176 46 177 45 178, that can be strung together to fill in gaps with some transitional terms.

The failure that seems most likely is that the stable beginning of the sequence, as L is increased, is strictly increasing, with that hole-filling postponed without limit.

I might be saying the same thing but I can't tell.

 rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: "franktaw at netscape.net" <franktaw at netscape.net>
> To: seqfan at list.seqfan.eu
> Sent: Wed, March 10, 2010 11:37:54 PM
> Subject: [seqfan] Re: seqs whose |differences| are 1,2,3,4,...
> Neil,
> Did you miss my note?  There is no lexicographically least permutation 
> with the specified difference property.  There are many permutations 
> with the property, but the greatest lower bound of these permutations 
> is the sequence Raff describes, and this is one-to-one but not onto.
> There may be a sequence with the property such that the inverse 
> permutation is lexicographically least.  The algorithm I described is 
> "trying" to find this, but may not actually do so.
> Franklin T. Adams-Watters
> P.s. The sequence from Ron cannot be continued.  The next term must be 
> 158; after that would have to be 4 or 312, both of which have already 
> been seen.

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