[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:
>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


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