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Irregular array of odd numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.
4

%I #11 Mar 19 2013 11:59:39

%S 1,3,5,13,21,7,11,17,9,15,23,35,53,85,19,29,45,69,75,113,25,37,61,93,

%T 141,151,213,227,341,33,49,51,77,81,117,181,201,277,301,453,43,65,67,

%U 99,101,149,163,241,245,267,369,373,401,403,565,605,853,909,1365

%N Irregular array of odd 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 These are the odd numbers in A222599. Sequence A222753 gives the length of the rows.

%H T. D. Noe, <a href="/A222752/b222752.txt">Rows n = 0..19 of irregular triangle, flattened</a>

%e The rows are

%e {1},

%e {},

%e {},

%e {3, 5},

%e {},

%e {13, 21},

%e {7, 11, 17},

%e {9, 15, 23, 35, 53, 85},

%e {19, 29, 45, 69, 75, 113},

%e {25, 37, 61, 93, 141, 151, 213, 227, 341},

%e {33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453}

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; 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, 1, 2^(nn - 1), 2}]; t

%Y Cf. A222753, A222754, A222755.

%K nonn,tabf

%O 0,2

%A _T. D. Noe_, Mar 04 2013