[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]

Correction of my previous posting (sorry for the confusion):
The code demonstrates that there are no *primes* in the range 7<=p<3491
(upper limit growing) in A086748. I've run it to verify the Resta comment apart 
also for the composites m< 1000 but not yet for 847 =7*11^2 (that's the only
number left in the range m<1000 that may need his k=7412629 for a solution).
My code is still running (a day on a single maple 9 thread...)
to find an odd k for 847=7*11 and 1001=7*11*13.

The odd-k solutions for the other m<1000 are much smaller than 7 million:
m=637=7^2*13 k=831159
m=893=19*47 k=433969
m=559=13*43 k=407135
m=749=7*107 k=394551
m=539=7^2*11 k=387369
m=763=7*109 k=373257
m=287=7*41 k=358549
m=737=11*67 k=351551
m=667=23*29 k=321321
m=851=23*37 k=305815

I need to figure out ways to speed up the modulo reduction of C(2k,k)
for k above 1 million to compete here (and I don't know
how much time Giovanni spent on this or whether he attempted to get a k-value
that solves m=1001)