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A222599 Irregular array of numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.

%I A222599 #10 Mar 18 2013 22:00:39
%S A222599 1,2,4,3,5,8,6,10,16,12,13,20,21,32,7,11,17,24,26,40,42,64,9,14,15,22,
%T A222599 23,34,35,48,52,53,80,84,85,128,18,19,28,29,30,44,45,46,68,69,70,75,
%U A222599 96,104,106,113,160,168,170,256,25,36,37,38,56,58,60,61,88
%N A222599 Irregular array of numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.
%C A222599 Note that row n ends with 2^n. The length of row n is A213678(n).
%H A222599 T. D. Noe, <a href="/A222599/b222599.txt">Rows n = 0..19 of irregular triangle, flattened</a>
%e A222599 The rows are
%e A222599 {1},
%e A222599 {2},
%e A222599 {4},
%e A222599 {3, 5, 8},
%e A222599 {6, 10, 16},
%e A222599 {12, 13, 20, 21, 32},
%e A222599 {7, 11, 17, 24, 26, 40, 42, 64},
%e A222599 {9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128}
%t A222599 Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 10; t = Table[{}, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, AppendTo[t[[diff + 2]], n]], {n, 2^(nn - 1)}]; Flatten[t]
%Y A222599 Cf. A213678 (number of terms in each row).
%K A222599 nonn,tabf
%O A222599 0,2
%A A222599 _T. D. Noe_, Mar 04 2013