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%I #18 Jan 13 2019 03:23:45
%S 1,2,3,4,6,8,12,13,16,17,20,25,33,34,36,37,39,40,42,48,50,52,59,60,62,
%T 66,67,69,71,76,80,81,83,86,89,95,99,101,103,104,107,109,117,118,120,
%U 121,122,125,126,132,133,134,135,136,137,139,142,143,145,149,152,157
%N Starting numbers x for which the trajectory of x->R(A006370(x)) ends in the cycle 1->4->2->1.
%C Define the map x-> A004086(A006370(x)) = E(x), which is the 3x+1 "Collatz" operation followed by digit reversal.
%C Examples of trajectories starting from small integers are:
%C 1->4->2->1->4->2->1->4->2->1->4->
%C 2->1->4->2->1->4->2->1->4->2->1->
%C 3->1->4->2->1->4->2->1->4->2->1->
%C 4->2->1->4->2->1->4->2->1->4->2->
%C 5->61->481->4441->42331->499621->4688941->42866041->421895821->...
%C 6->3->1->4->2->1->4->2->1->4->2->
%C 7->22->11->43->31->49->841->4252->6212->6013->4081->44221->466231->4968931->..
%C 8->4->2->1->4->2->1->4->2->1->4->
%C 9->82->14->7->22->11->43->31->49->841->4252->->6212->6013->4081->44221->
%C 10->5->61->481->4441->42331->499621->4688941->42866041->...
%C 11->43->31->49->841->4252->6212->6013->4081->44221->466231->
%C 12->6->3->1->4->2->1->4->2->1->4->
%C 13->4->2->1->4->2->1->4->2->1->4->
%C 14->7->22->11->43->31->49->841->4252->6212->6013->->4081->44221->466231->
%C 15->64->23->7->22->11->43->31->49->841->4252->
%C 16->8->4->2->1->4->2->1->4->2->1->
%C 17->25->67->202->101->403->121->463->931->4972->6842->->1243->373->211->436->
%C 18->9->82->14->7->22->11->43->31->49->841->
%C 19->85->652->623->781->4432->6122->1603->184->29->88->
%C 20->1->4->2->1->4->2->1->4->2->1->
%C When the trajectory of E(n) doesn't reach 1, it
%C (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
%C (ii) 247 and from there keeps indefinitely this value, or
%C (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.
%C There is also a 7-cycle: 320281 -> 448069 -> 8024431 -> 49237042 -> 12581642 -> 1280926 -> 364046 -> 320281. - _Charlie Neder_, Jan 12 2019
%e As commented above, starting from 1 to 4 enters the 4-cycle, so the first 4 integers are added to the sequence. Starting from 5, the trajectory grows indefinitely (does not enter the 4-cycle), so 5 is not added to the sequence.
%Y Cf. A004086, A006370, A006577.
%K easy,base,nonn
%O 1,2
%A Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), May 25 2007
%E Edited by _R. J. Mathar_, Oct 02 2009
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