

A222297


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


2



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
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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



