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A222752 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.

%I A222752 #11 Mar 19 2013 11:59:39
%S A222752 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 A222752 141,151,213,227,341,33,49,51,77,81,117,181,201,277,301,453,43,65,67,
%U A222752 99,101,149,163,241,245,267,369,373,401,403,565,605,853,909,1365
%N A222752 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 A222752 These are the odd numbers in A222599. Sequence A222753 gives the length of the rows.
%H A222752 T. D. Noe, <a href="/A222752/b222752.txt">Rows n = 0..19 of irregular triangle, flattened</a>
%e A222752 The rows are
%e A222752 {1},
%e A222752 {},
%e A222752 {},
%e A222752 {3, 5},
%e A222752 {},
%e A222752 {13, 21},
%e A222752 {7, 11, 17},
%e A222752 {9, 15, 23, 35, 53, 85},
%e A222752 {19, 29, 45, 69, 75, 113},
%e A222752 {25, 37, 61, 93, 141, 151, 213, 227, 341},
%e A222752 {33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453}
%t A222752 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 A222752 Cf. A222753, A222754, A222755.
%K A222752 nonn,tabf
%O A222752 0,2
%A A222752 _T. D. Noe_, Mar 04 2013