

A222599


Irregular array of 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, 2, 4, 3, 5, 8, 6, 10, 16, 12, 13, 20, 21, 32, 7, 11, 17, 24, 26, 40, 42, 64, 9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128, 18, 19, 28, 29, 30, 44, 45, 46, 68, 69, 70, 75, 96, 104, 106, 113, 160, 168, 170, 256, 25, 36, 37, 38, 56, 58, 60, 61, 88
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OFFSET

0,2


COMMENTS

Note that row n ends with 2^n. The length of row n is A213678(n).


LINKS



EXAMPLE

The rows are
{1},
{2},
{4},
{3, 5, 8},
{6, 10, 16},
{12, 13, 20, 21, 32},
{7, 11, 17, 24, 26, 40, 42, 64},
{9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128}


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 10; 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, 2^(nn  1)}]; Flatten[t]


CROSSREFS

Cf. A213678 (number of terms in each row).


KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



