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

0,2

Comments

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

Links

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

Example

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}

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]

Crossrefs

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

Sequence in context: A187790 A307613 A279343 * A249683 A360434 A215898

Adjacent sequences: A222596 A222597 A222598 * A222600 A222601 A222602

Keyword

nonn,tabf

Author

T. D. Noe, Mar 04 2013

Status

approved