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

Richard J. Mathar mathar at mpia-hd.mpg.de
Thu Jul 11 15:36:38 CEST 2024


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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