[seqfan] Re: Sturdy and flimsy numbers.
T. D. Noe
noe at sspectra.com
Sun Dec 20 19:51:32 CET 2009
>I followed an A-number from one frame of the OEIS movie,
>and found this:
>http://www.research.att.com/~njas/sequences/A125121
>
>
>Just wondering, how well-defined this kind of sequence is?
>
>That is, is there some absolute upper limit of k for each n,
>after which the program can finish the testing loop?
Although theorem 2.1 in the paper by Stolarsky is useful, the seqfan e-mail
from Jack Brennen sometime near July 2008 is the key to computing these
numbers. According to my notes, his e-mail says:
"To determine if an odd number N is flimsy, take the finite set of residues
of 2^a (mod N). Assume that the number of 1's in the binary representation
of N is equal to C. To show that the number is flimsy, find a way to
construct zero (mod N) by adding up some number of residues of 2^a (mod N)
using less than C terms. To show that the number is sturdy, show that it's
impossible to do so."
The bottom line is that this sequence, though difficult to compute, is well
defined.
Tony
More information about the SeqFan
mailing list