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

1,2

Comments

Sequence A222118 gives the number of terms in each row.

Links

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

Example

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}

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]

Crossrefs

Cf. A222118.

Sequence in context: A039875 A206555 A110539 * A211981 A019997 A263875

Adjacent sequences: A222294 A222295 A222296 * A222298 A222299 A222300

Keyword

nonn,tabf

Author

T. D. Noe, Feb 23 2013

Status

approved