A222297 Irregular triangle of numbers first appearing in the Collatz (3x+1) iteration of n.

1, 2, 3, 4, 5, 8, 10, 16, 6, 7, 11, 13, 17, 20, 22, 26, 34, 40, 52, 9, 14, 28, 12, 15, 23, 35, 46, 53, 70, 80, 106, 160, 18, 19, 29, 44, 58, 88, 21, 32, 64, 24, 25, 38, 76, 27, 31, 41, 47, 61, 62, 71, 82, 91, 92, 94, 103, 107, 121, 122, 124, 137, 142, 155, 161

Offset: 1

Author

T. D. Noe, Feb 23 2013

Keywords

• nonn
• tabf

Comments

Sequence A222118 gives the number of terms in each row.

Examples

			The irregular table begins
{1},
{2},
{3, 4, 5, 8, 10, 16},
{},
{},
{6},
{7, 11, 13, 17, 20, 22, 26, 34, 40, 52},
{},
{9, 14, 28},
{},
{},
{12},
{},
{},
{15, 23, 35, 46, 53, 70, 80, 106, 160}
		

Links

• T. D. Noe, Rows n = 1..4000 of irregular triangle, flattened

Crossrefs

Cf. A222118.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; found = {}; t = Table[c = Collatz[n]; r = Complement[c, found]; found = Union[found, c]; r, {n, 27}]; Flatten[t]