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Define the map x-> A004086(A006370(x)) = E(x), which is the 3x+1 "Collatz" operation
followed by digit reversal. Examples of trajectories starting from small
integers are:
1->4->2->1->4->2->1->4->2->1->4->
2->1->4->2->1->4->2->1->4->2->1->
3->1->4->2->1->4->2->1->4->2->1->
4->2->1->4->2->1->4->2->1->4->2->
5->61->481->4441->42331->499621->4688941->42866041->421895821->...
6->3->1->4->2->1->4->2->1->4->2->
7->22->11->43->31->49->841->4252->6212->6013->4081->44221->466231->4968931->..
8->4->2->1->4->2->1->4->2->1->4->
9->82->14->7->22->11->43->31->49->841->4252->->6212->6013->4081->44221->
10->5->61->481->4441->42331->499621->4688941->42866041->...
11->43->31->49->841->4252->6212->6013->4081->44221->466231->
12->6->3->1->4->2->1->4->2->1->4->
13->4->2->1->4->2->1->4->2->1->4->
14->7->22->11->43->31->49->841->4252->6212->6013->->4081->44221->466231->
15->64->23->7->22->11->43->31->49->841->4252->
16->8->4->2->1->4->2->1->4->2->1->
17->25->67->202->101->403->121->463->931->4972->6842->->1243->373->211->436->
18->9->82->14->7->22->11->43->31->49->841->
19->85->652->623->781->4432->6122->1603->184->29->88->
20->1->4->2->1->4->2->1->4->2->1->
When the trajectory of E(n) doesn't reach 1, it (i) either reaches 238 and from there
enters the 18 steps cycle 911, 4372, 6812, 6043, 3181, 4459, 87331, 449162, 185942,
17929, 88375, 602662, 133103, 8914, 7544, 2773 or
(ii) 247 and from there keeps indefinitely this value, or
(iii) it reaches an integer with 4 the most significant digit and 1 the least significant digit
and from there keeps this structure and grows indefinitely; there is
no other pair of digits with this peculiarity.
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