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

franktaw at netscape.net franktaw at netscape.net
Fri Mar 12 22:28:09 CET 2010

The lexicographically first sequence must start with 0 (if working with 
the non-negative integers.  If working with the positive integers, just 
add 1 to everything).

Franklin T. Adams-Watters

-----Original Message-----
From: N. J. A. Sloane <njas at research.att.com>

Robert Munafo said:

> I have established a webpage for this sequence at
> http://mrob.com/pub/math/seq-a171884.html

Me:  At beginning of the page it says:

"First Few Terms: The sequence starts with 0 and 1, then 3 because 
1+2=3. ..."

This is not necessarily true.
The sequence could also begin 1 0 2 5 9 ... (say) which has |diffs|
1,2,3,4,...  There is no necessity to begin with 0.

(Incidentally in the original problem the sequence is
required to be a permutation of the numbers 1,2,3,...,
not 0,1,2,3,4,..., so that both the sequences and its
|differences| consists of the numbers 1,2,3,...,
And likewise there is no necessity to begin with 1.)



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