If you look at what this operation does to 1 2 3 4 ... you get 1, 3, 1, 5, 3, 7, 1, 9, 5, 13, 3, 11, 7, 15, 1, 17, 9, 25, 5, 21, 13, 29,... which is A030101 This has a different definition from yours: it doesn't add 1 before reversing. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Sep 29, 2015 at 10:14 AM, Allan Wechsler <acwacw@gmail.com> wrote:
5 bits: a single cycle of 32, unless I screwed up.
On Tue, Sep 29, 2015 at 9:59 AM, Allan Wechsler <acwacw@gmail.com> wrote:
In general, add one and then permute the bits (according to some fixed permutation) seems like it can have very complicated dynamics.
On Tue, Sep 29, 2015 at 9:55 AM, Allan Wechsler <acwacw@gmail.com> wrote:
This is fairly cool. 1 bit: a single 2-cycle. 2 bits: 1+3 = 4.
3 bits: a single cycle of 8.
4 bits: 4+5+7 = 16.
How far have you gone?
On Tue, Sep 29, 2015 at 9:49 AM, James Propp <jamespropp@gmail.com> wrote:
I've been playing with the compound operation on bit-strings of length m in which you (a) add 1 mod 2^m and (b) reverse the order of the bits.
Has anyone seen this before? It seems sufficiently simple that I doubt I'm the first person to have played with it.
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