02/18/2013, 11:08 PM
Notice that 1.51... is NOT a real repelling fixpoint of x=3^x-2^x.
The only fixpoints of x=3^x-2^x on the extended real line are 0,1 and +oo.
The value 1 seems to suggest that f(2)=1.51... might make the sequence oscillate around 1.
Assuming the above it might work to compute 1.51... by starting at value 1 and doing the iterations backwards until we reach approximately 0. But of course nicer ways should be available.
I have not seen this sequence investigated before and it seems it might require new ideas, unless I overlooked something trivial.
I must add that this thread also deserves some credit from my student mick who some of you have already met on MSE.
Mick and I have given eachother permission to post eachothers (or common ) ideas concerning some math subjects including dynamical systems and tetration.
The only fixpoints of x=3^x-2^x on the extended real line are 0,1 and +oo.
The value 1 seems to suggest that f(2)=1.51... might make the sequence oscillate around 1.
Assuming the above it might work to compute 1.51... by starting at value 1 and doing the iterations backwards until we reach approximately 0. But of course nicer ways should be available.
I have not seen this sequence investigated before and it seems it might require new ideas, unless I overlooked something trivial.
I must add that this thread also deserves some credit from my student mick who some of you have already met on MSE.
Mick and I have given eachother permission to post eachothers (or common ) ideas concerning some math subjects including dynamical systems and tetration.