[seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."

Richard Guy rkg at cpsc.ucalgary.ca
Mon Aug 16 18:06:35 CEST 2010

```Where angels fear to tread.  OEIS has left me behind years ago,
and I never learned how it dealt with doubly infinite sequences.

The triangular numbers are

... 28, 21, 15, 10, 6, 3, 1, 0, 0, 1, 3, 6, 10, 15, 21, ...

The squares are

... 25, 16, 9, 4, 1, 0, 1, 4, 9, 19, 25, ...

The pentagonal numbers are got by dividing the triangular numbers
by 3:

0/3 = 0, 1/3 = ?, 3/3 = 1, 6/3 = 2, 10/3 = ?, 15/3 = 5, 21/3 = 7, ...

and their proper(?) arrangement is

..., 57, 40, 26, 15, 7, 2, 0, 1, 5, 12, 22, 35, 51, 70, ...

The hexagonal numbers are the triangular numbers!

..., 78, 55, 36, 21, 10, 3, 0, 1, 6, 15, 28, 45, 66, ...

etc.   Sorry to be so confused (or confusing?), but I never
did know what `offset' meant, anyway!      R.

On Mon, 16 Aug 2010, Alonso Del Arte wrote:

> From a purely logistical point of view, I would say start with a(0) = 0.
> Most of us on this list know well enough to start a search from a(2) or
> a(3), but I'm sure some people will search for the triangular numbers as "0,
> 1, 3, 6, 10, 15, 21," and such.
>
> Al
>
> On Mon, Aug 16, 2010 at 12:38 AM, N. J. A. Sloane <njas at research.att.com>wrote:
>
>> point for the figurate numbers.
>>
>> My feeling is that there is no solution that is perfect,
>> and so we might as well leave the offsets the way they are
>> (provided they are not actually wrong).
>>
>> It is impossible to be 100% consistent!
>>
>>
>>  Best regards
>>                         Neil
>>
>>
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```