S(n) isn't a good name because it can be confused with regular maximum shifts function. Ikosarakt1 (talk ^ contribs) 03:52, September 23, 2015 (UTC)
But this function is precisely the regular maximum shifts function. LittlePeng9 (talk) 04:52, September 23, 2015 (UTC)
lol -- vel! 00:44, September 24, 2015 (UTC)
Talking about names[]
S(n) isn't a good name, as it can be confused by both maximum shifts function and the successor function and most summation functions. 80.98.179.160 18:26, November 10, 2017 (UTC)
- Either way, this notation is standard now - regardless of the name, S(n) notation is the one universally used to refer to this function. LittlePeng9 (talk) 19:27, November 10, 2017 (UTC)
S(6) research[]
I'm not sure and haven't yet thought of a proof of my claim but I think that given some really strong system of pure number theory, we can find a 6 state 2 colour turing machine that we can prove in a stronger system can never be proven in that system to never halt on a blank input and does not halt after fewer steps than any turing machine with any input with finitely many nonblank slots can be proven in that system within a googol characters to eventually halt. If that turing machine does eventually halt, then S(6) is unfathomably larger than the current record holder for the 6 state 2 colour turing machine. Blackbombchu (talk) 18:26, October 12, 2018 (UTC)