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

0,2

Comments

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

Links

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

Example

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}

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

Crossrefs

Cf. A222753, A222754, A222755.

Sequence in context: A249340 A034484 A290441 * A172143 A218790 A168388

Adjacent sequences: A222749 A222750 A222751 * A222753 A222754 A222755

Keyword

nonn,tabf

Author

T. D. Noe, Mar 04 2013

Status

approved