[seqfan] Re: Need help with Escott sequence from 1903

[Allan Wechsler]

The most obvious interpretation is that the sequence is all numbers y such
that y^2 - 1 is the sum of two positive squares.

That would be A050795.

In fact, the *only* discrepancies between A050795 and the mystery sequence
A350978 (as far as it goes) are that the former includes 17 and the latter
excludes it, and that the former excludes 31 and the latter includes it.

My feeling is that Escott, or the pseudonymous editor "Carvyge", or some
other person involved in preparing this issue of IdM for the press,  made
an error, and that the intended sequence *was* A050795.

(Disclaimer: I compared the two sequences by eye, and might have missed
something.)

On Sun, Mar 6, 2022 at 10:08 PM Neil Sloane <njasloane at gmail.com> wrote:

> Dear Sequence Fans, I have been going through photocopies of articles
> from L'Intermédiaire
> des Mathématiciens that I made 50 years ago.
>
> There is one sequence that is a mystery, A350978, from
> E.-B. Escott, Query 2521 <https://oeis.org/A350978/a350978.pdf>,
> L'Intermédiaire des Mathématiciens, 10 (1903), 285.
> You can see a scan of this page in the entry A350978. The original note
> from Escott was written in English, but the journal translated it into
> French, and the translation is hard to understand (my guess is the English
> was also hard to understand).
>
> We have 33 terms, computed by a famous American number theorist, with a
> fuzzy definition. Could someone work backwards, and recover the correct
> definition?
>
> Or, go to some library that carries this journal (I saw it at Brown
> University), and  find all the references to Query 2521. Each Query would
> be mentioned several times in successive volumes.
> The I.D.M. was like slow-motion email.
>
> For other "new" sequences from this journal, work backwards from A350978
> (and forwards - I still have another 50 pages of xeroxes to work through)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
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