# [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>
wrote:

> 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
problem.

--
Robert Munafo  --  mrob.com

```