

A224367


Triangle read by rows giving trajectory of k/(2n+1) in Collatz problem, k = 1..2n.


0



0, 1, 2, 4, 5, 7, 6, 9, 10, 11, 11, 13, 12, 4, 5, 1, 6, 3, 2, 4, 7, 8, 9, 8, 10, 11, 9, 13, 11, 13, 12, 14, 15, 5, 16, 16, 6, 18, 17, 20, 17, 19, 7, 4, 5, 4, 6, 1, 5, 6, 7, 7, 2, 9, 6, 8, 7, 17, 18, 9, 19, 9, 10, 20, 20, 11, 10, 22, 11, 24, 21, 23, 21, 36, 37
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OFFSET

0,3


COMMENTS



LINKS



EXAMPLE

The 2nd row [4, 5, 7, 6] gives the number of iterations of k/5 (the first element is not counted):
k=1 => 1/5 >2/5 > 1/5 > 8/5 > 4/5 with 4 iterations;
k=2 => 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 5 iterations;
k=3 => 3/5 > 4/5 > 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 7 iterations;
k=4 => 4/5 > 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 6 iterations.
The array starts:
[0];
[1, 2];
[4, 5, 7, 6];
[9, 10, 11, 11, 13, 12];
[4, 5, 1, 6, 3, 2, 4, 7];
...


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[Numerator[#]], #/2, 3 # + 1] &, n, UnsameQ, All]; t = Join[{{0}}, Table[s = Collatz[k/(2*n + 1)]; len = Length[s]  2; If[s[[1]] == 2, len = len  1]; len, {n, 10}, {k, 2*n}]]; Flatten[t] (* program from T. D. Noe, adapted for this sequence  see A210483 *).


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



