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

Author

T. D. Noe, Mar 04 2013

Keywords

• nonn
• tabf

Comments

Note that row n ends with 2^n. The length of row n is A213678(n).

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

• T. D. Noe, Rows n = 0..19 of irregular triangle, flattened

Crossrefs

Cf. A213678 (number of terms in each row).

Programs

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]