Tomás Oliveira e Silva's mappings

On the page Computational verification of the 5x+1 and 7x+1 conjectures, Tomás Oliveira e Silva introduced mappings T5 and T7 of ℤ into ℤ:

It is believed that the iterates of these functions eventually enter one of the cycles listed below. We print the iterates and the number of steps taken to reach a cycle is recorded.

Cycles for T5:

(i) 1,6,3,1 (ii) -1,-4,-2,-1 (iii) -7,-34,-17,-84,-42,-21,-7.

Cycles for T7:

(i) 1,8,4,2,1
(ii)-1,-6,-3,-1
(iii) -11,-76,-38,-19,-132,-66,-33,-11
(iv) -509,-3562,-1781,-12466,-6233,-43630,-21815,-4363,-30540,-15270,-7635,-2545,-509
(v) -701,-4906,-2453,-17170,-8585,-1717,-12018,-6009,-2003,-14020,-7010,-3505,-701
(vi) -961,-6726,-3363,-1121,-7846,-3923,-27460,-13730,-6865,-1373,-9610,-4805,-961.

Also see Generalized 3x+1 functions and Markov matrices.

Enter y:
Mapping T5
Mapping T7

Last modified 26th August 2011
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