[seqfan] Subject: Need help computing a number

[Neil Sloane]

Dear Math Fun, Sequence Fans,

Start with an integer k, 13 say, and repeatedly double it and add 1 until
reaching a prime:

13 -> 27 -> 55 -> 111 -> 223.

This took 4 steps, so we set R(13) = 4. This is called Riesel's problem,
and if we never reach a prime we set R(k) = 0. The sequence R(k) is A050412.
I think Riesel showed R(509203) = 0, and it seems it is believed that R(k)
!= 0 for k<509203.

For another sequence (A374965) that Harvey Dale and I have been studying,
we badly need the value of R(104916). Can someone help?  If 104916 takes m
steps, the prime reached will be 104917*2^m - 1,

so we don't actually need to see the prime (just m).

I ran a naive Mathematica program (from A050412) on my iMAC, but I killed
it after nearly 24 hours.

 I have no idea how far it got.  The bottleneck is presumably the primality
testing, but I don't know who has the fastest program for that.
Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com