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%I #10 Mar 18 2013 22:00:39
%S 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 23,34,35,48,52,53,80,84,85,128,18,19,28,29,30,44,45,46,68,69,70,75,
%U 96,104,106,113,160,168,170,256,25,36,37,38,56,58,60,61,88
%N 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 Note that row n ends with 2^n. The length of row n is A213678(n).
%H T. D. Noe, <a href="/A222599/b222599.txt">Rows n = 0..19 of irregular triangle, flattened</a>
%e The rows are
%e {1},
%e {2},
%e {4},
%e {3, 5, 8},
%e {6, 10, 16},
%e {12, 13, 20, 21, 32},
%e {7, 11, 17, 24, 26, 40, 42, 64},
%e {9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128}
%t 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 Cf. A213678 (number of terms in each row).
%K nonn,tabf
%O 0,2
%A _T. D. Noe_, Mar 04 2013
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