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A222752
Irregular array of odd numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.
4
1, 3, 5, 13, 21, 7, 11, 17, 9, 15, 23, 35, 53, 85, 19, 29, 45, 69, 75, 113, 25, 37, 61, 93, 141, 151, 213, 227, 341, 33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453, 43, 65, 67, 99, 101, 149, 163, 241, 245, 267, 369, 373, 401, 403, 565, 605, 853, 909, 1365
OFFSET
0,2
COMMENTS
These are the odd numbers in A222599. Sequence A222753 gives the length of the rows.
EXAMPLE
The rows are
{1},
{},
{},
{3, 5},
{},
{13, 21},
{7, 11, 17},
{9, 15, 23, 35, 53, 85},
{19, 29, 45, 69, 75, 113},
{25, 37, 61, 93, 141, 151, 213, 227, 341},
{33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453}
MATHEMATICA
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; 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, 1, 2^(nn - 1), 2}]; t
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Mar 04 2013
STATUS
approved