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.
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, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128, 18, 19, 28, 29, 30, 44, 45, 46, 68, 69, 70, 75, 96, 104, 106, 113, 160, 168, 170, 256, 25, 36, 37, 38, 56, 58, 60, 61, 88
Offset: 0
Examples
The rows are
{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, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128}
Links
Crossrefs
Cf. A213678 (number of terms in each row).
Programs
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Mathematica
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]
Comments