Tetration based 1.4447

[hypcos]

> OmegaNum(1.4447).tetr(101)+''
< '2.6717465674555796'
> OmegaNum(1.4447).pow(OmegaNum(1.4447).tetr(100))+''
< '2.672301459237309'

I expect that those two have similar result, but the former seems to be 1.4447^^100 instead of 1.4447^^101.

[Naruyoko]

This seems to be caused by the limit on the number of iterations of pow (set to 100) before exiting. OmegaNum(1.4447).tetr(b) for b>100 fits this limit, which sets f (layers to add left) to 0. However, 1.4447^^b does not converge as b->∞. Indeed, taking power iteratively yeilds 1.4447^^572=e5.557991388727991e6489802081. This requires the limit to be set to at least 573 though since we are checking for r reaching e9e15 to exit the loop.

I am not sure how to solve this. Increasing this limit isn't really a solution because it would severely degrade the speed if the base is slightly above the upper limit for convergence (e^e^-1 for iteration).