[seqfan] Re: permutation of nonnegative integers

[jnthn stdhr]

On Wed, Apr 11, 2018 at 7:27 PM, Neil Sloane <njasloane at gmail.com> wrote:



>
> BTW, could you elaborate on "Increment a and b".  What exactly does that
> mean?
>
>
Add one to a and b, then repeat:

Start with a=0 and b=1. Create the set of four numbers [0, 0+1, 0*1, 1].
Add 0 and 1 to the sequence, so S={0,1}
a=1, b=2 ->   [1, 1+2, 1*2, 2].  Add 3 and 2 to the sequence, so S={0,1,3,2}
a=2, b=3 ->   [2, 2+3, 2*3, 3].  Add 5 and 6 to the sequence, so
S={0,1,3,2,5,6}
a=3, b=4 ->   [3, 3+4, 3*4, 4].  Add 7 and 12 and 4 to the sequence, so
S={0,1,3,2,5,6,7,12,4}
.
.
.

I left out the first term A024701(1) = 2 in my original messege, so what I
said holds for all 49 terms in A024701.  Maybe A024701 should be
extended?  Also,
I noticed that if a(n) is a power of 2 then a(n+1) = 2*a(n)+1.  Maybe these
connections are obvious from the sequence definition.

-Jonathan