User blog:Moooosey/dco + decord sequence

Today I shall share my most recent creation and a demonstration of its power.

Decord sequences
The definition of a decord sequence is this:

Yes, I know you hate ellipses. So here's a definition that you'll like better:

Then I defined dco(a) = the length of a decord sequence starting at a.

then I made a demonstrative function, defined as dco(gamma_0+n). After some discussion, conwaylife.com forum user BlinkerSpawn agreed with me that it was comparable to f_gamma_0(n). (specifically, that it was at least comparable to f_gamma_0(n-a) for small a).

As a demonstration, here's the beginning of the decord sequence of gamma_0+1:

and so forth. Presumably, dco(gamma_0+n) exceeds things like graham's number or even hydra(any small value) at even rather low n, since f_gamma_0(n) is of course considerably more powerful than f_e_0(n)