continued fraction convergents for sqrt(2)^sqrt(2) start 1, 2, 3/2, 5/3, 13/8, 18/11, 31/19, 80/49, 191/117, 271/166, 2901/1777, 3172/1943, 6073/3720, 9245/5663, ... On Sun, Apr 22, 2018 at 4:44 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:

I think there was a discussion about 'nearest rationals to pi' ... and I think there's a 'sequence' about that somewhere.

I'd be interested in an algorithm to generate such sequences, ...

and I'd like to see what results it gives for sqrt(2)^sqrt(2)

... a number which has a specific role in proving that a^b can be rational even if 'a' and 'b' are not [see, e.g., The Princeton Companion]

Guy

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