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%I #10 Mar 25 2013 14:21:30
%S 15,30,60,120,151,239,240,255,302,377,423,425,478,479,480,510,593,604,
%T 669,685,743,754,755,846,847,850,851,939,956,958,960,1020,1053,1057,
%U 1186,1191,1208,1297,1321,1338,1341,1370,1375,1473,1486,1487,1508,1509,1510
%N Numbers whose Collatz trajectory contains equal number of terms of the form 4k+1 and 4k+3.
%H T. D. Noe, <a href="/A217744/b217744.txt">Table of n, a(n) for n = 1..10000</a>
%t Collatz[n_] :=NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], Mod[#, 4] == 1 &]] -Length[Select[Collatz[n], Mod[#, 4] == 3 &]] == 0, AppendTo[t, n]], {n, 1500}]; t
%Y Cf. A070165, A192719, A217743.
%K nonn
%O 1,1
%A _Jayanta Basu_, Mar 23 2013