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 A129121 Starting numbers x for which the trajectory of x->R(A006370(x)) ends in the cycle 1->4->2->1. 3
 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, 66, 67, 69, 71, 76, 80, 81, 83, 86, 89, 95, 99, 101, 103, 104, 107, 109, 117, 118, 120, 121, 122, 125, 126, 132, 133, 134, 135, 136, 137, 139, 142, 143, 145, 149, 152, 157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE 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. CROSSREFS Cf. A006577. Sequence in context: A211397 A173542 A085113 * A018556 A018387 A029449 Adjacent sequences:  A129118 A129119 A129120 * A129122 A129123 A129124 KEYWORD easy,base,nonn AUTHOR Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), May 25 2007 EXTENSIONS Edited by R. J. Mathar, Oct 02 2009 STATUS approved

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