[seqfan] Re: More terms for needed for A086748, Numbers m such that when C(2k, k) == 1 (mod m) then k is necessarily even.

[israel at math.ubc.ca]

There is also a problem with the Name of this sequence. "Numbers m such 
that when C(2k, k) == 1 (mod m) then k is necessarily even".

If m is even, according to Wang's first comment C(2k,k) == 1 (mod m) can't 
ever happen, and the conditional statement "when ... then ..." is vacuously 
true. That would mean that all even m should be terms of the sequence, not 
that none of them are.

I suggest changing the Name to "Odd numbers m such that ...".

Cheers,
Robert

On Jul 11 2024, Richard J. Mathar wrote:

> The Resta comment in A086748 seems to say that all numbers of the form 
> 3*(2*t-1) and 5*(2*t-1) are in the sequence (as a consequence of the Wang 
> comment), and that numbers m<1000 which are not of that form are not in 
> the sequence, because he has found a counterexample/solution with odd k 
> <= 7412629 for each of these. That means all terms m<=1000 in A086748 are 
> known to be either in or not to be in the sequence, although only terms 
> m<=245 are shown. (That is: terms of A007775 < 1000 are not in A086748 by 
> pure numerical brute force experimentation).
>
> The Resta comment in A086748 uses a confusing dangling "either". I think 
> the intended meaning is
>
> "All numbers of the form 3*(2*t-1) and 5*(2*t-1) are in the sequence (as 
> a consequence of the Wang comment), and all other odd numbers (7-rough 
> numbers) m<1000 are absent because for these odd k <= 7412629 can be 
> found that solve C(2k,k) == 1 (mod m)."
>
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