[seqfan] A177045: ordering of expressions built from numbers 2 and exponentiations

[Vladimir Reshetnikov]

Hello seqfans,

Can anybody suggest an effective way to calculate elements of A177045?
Currently I need to manually prove that each element is in the correct
position - and I do not see any general way to do it so that I can
generate elements of this sequence with an algorithm. I believe it is
closely related to A002845, although I do not think that there is a
formula connecting them. And please, check that I provided correct
initial elements of the sequence.

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Thanks
Vladimir Reshetnikov