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.

1, 3, 5, 13, 21, 7, 11, 17, 9, 15, 23, 35, 53, 85, 19, 29, 45, 69, 75, 113, 25, 37, 61, 93, 141, 151, 213, 227, 341, 33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453, 43, 65, 67, 99, 101, 149, 163, 241, 245, 267, 369, 373, 401, 403, 565, 605, 853, 909, 1365

Offset: 0

Author

T. D. Noe, Mar 04 2013

Keywords

• nonn
• tabf

Comments

These are the odd numbers in A222599. Sequence A222753 gives the length of the rows.

Examples

			The rows are
{1},
{},
{},
{3, 5},
{},
{13, 21},
{7, 11, 17},
{9, 15, 23, 35, 53, 85},
{19, 29, 45, 69, 75, 113},
{25, 37, 61, 93, 141, 151, 213, 227, 341},
{33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453}
		

Links

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

Crossrefs

Cf. A222753, A222754, A222755.

Programs

Mathematica

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