[seqfan] Re: new dragon conjecture

[brad klee]

> A112658, A122002, A125047, A343180

These don't seem to have repeats, so probably not. The simplest 
definition I could think of is this: 

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

a /@ Range[2^6]

{1, 1, 2, 1, 3, 2, 0, 1, 1, 3, 2, 2, 3, 0, 0, 1, 1, 1, 2, 
3, 3, 2, 0, 2, 1, 3, 2, 0, 3, 0, 0, 1, 1, 1, 2, 1, 3, 2, 0, 3, 1, 3, 
2, 2, 3, 0, 0, 2, 1, 1, 2, 3, 3, 2, 0, 0, 1, 3, 2, 0, 3, 0, 0, 1}

Meanwhile, the community post has been updated with digit-streaming 
algorithms for Sqrt[n] and Pi: 

https://community.wolfram.com/groups/-/m/t/3140560

The algorithm for Pi could be adapted to other cases where a 
sequence of rational approximants is known by p-recurrence. 

Whether those streaming algorithms actually qualify as spigots 
doesn't affect that they certainly work quicker than 1/4 second 
per iteration. This means that the data stream to the peripheral 
still needs delays added in so as not to move too quickly for 
human vision. 

 
Happy Pi day weekend, 


--Brad