Finitist Wrote:Hi. I've seen a sequence like that on Robert Munafo's site. Is yours related to Friedman sequences (nonrepeating sequences of different numbers of letters) as described below?

Right now I can't see how they would be related.

Finitist Wrote:I'd be interested to know what that function is that you're working on,

Hopefully this will be appearing in an undergrad journal...

The function

D goes from N -> N by way of finite tuples. Given n in N,

D takes n to the n-tuple of n's. So it would take 4 to (4,4,4,4) for example. Then (non-bold) D acts on that tuple by

D(n,n,...,n) = D(D(n,n,...,n-1),D(n,n,...,n-1)), so

D(4,4,4,4) = D(D(4,4,4,3),D(4,4,4,3)) for example.

When all those tuples are reduced to pairs, all the D's become A's for Ackermann.

In other words,

D(n) = D(n,n,...,n).

The expression A(A(A(61,61),A(61,61)), A(A(61,61),A(61,61))) is

D(3)