[seqfan] Re: new dragon conjecture

[Kevin Ryde]

brad klee via SeqFan <seqfan at list.seqfan.eu> writes:
>
>> A112658, A122002, A125047, A343180
> These don't seem to have repeats, so probably not.

Ah yes.  Actually no repeats is one of their motivations:
Infinite, alternating parity, square-free
(nowhere repeat E E for any block E.)

> a[n_ /; OddQ[n]] := Mod[(n + 1)/2, 4]
> a[n_ /; EvenQ[n]] := a[n/2]

I see that's two bits above the lowest 1 bit, such as

    a(n) = (A025480(n-1) + 1) mod 4
    where A025480(n) is all the bits above the lowest 0,
    and hence offset to turn lowest 1 into lowest 0

Plain paperfolding is one bit, such as

    A014707(n) = A025480(n) mod 2