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

Robert Munafo mrob27 at gmail.com
Sat Mar 13 00:07:33 CET 2010

On Fri, Mar 12, 2010 at 15:36, 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.

Thanks, Neil.

I have updated the page to explain that the precise sequence definition was
ambiguous because of the ambiguous phrase "natural numbers" and added a list
of the terms of what I am calling "A171884", before proceeding into the
"first few terms" explanation.

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.

Some other sequence might start that way, but not "A171884".

> (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.)

No, the original problem was "Consider all rearrangements of the natural
numbers with the property that..." Your clarification as to which definition
of "natural numbers" invokes a more precisely stated and therefore different

 Robert Munafo  --  mrob.com

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