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A specific value of the Ackermann function
#12
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)
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Messages In This Thread
large numbers - by bo198214 - 10/19/2008, 11:56 AM
RE: large numbers - by Finitist - 10/26/2008, 06:49 PM
RE: A specific value of the Ackermann function - by tetrator - 10/28/2008, 01:18 AM

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