A318907 Numbers m such that A006666(m)/A006667(m) is an integer.

5, 6, 10, 17, 20, 21, 24, 26, 40, 42, 44, 45, 46, 80, 84, 85, 96, 104, 106, 112, 113, 116, 117, 120, 122, 136, 138, 140, 141, 150, 151, 159, 160, 168, 170, 283, 288, 296, 298, 304, 308, 309, 320, 321, 324, 325, 326, 331, 336, 340, 341, 377, 384, 416, 424, 426

Offset

1,1

Comments

A006666 and A006667 are respectively the number of halving and tripling steps in the '3x+1' problem.

The corresponding integers are 4, 3, 5, 3, 6, 6, 4, 4, 7, 7, 3, 3, 3, 8, 8, 8, 5, 5, 5, 3, 5, 3, 3, 3, ...

The numbers of the form (4^k - 1)/3 for k > 1 (A002450) are in the sequence.

We observe subsets of consecutive numbers: (5, 6), (20, 21), (44, 45, 46), (84, 85), (112, 113), ...

Links

Table of n, a(n) for n=1..56.

Example

17 is in the sequence because A006666(17)/A006667(17) = 9/3 = 3 is integer.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 70; t = {}; n = 0; While[Length[t] < nn, n++; c = Collatz[n]; ev = Length[Select[c, EvenQ]]; od = Length[c] - ev - 1; If[od>0 && IntegerQ[ev/od], AppendTo[t, n]]]; t

Crossrefs

Cf. A002450, A006666, A006667, A277367, A281938.

Sequence in context: A096728 A329271 A011985 * A231503 A254227 A326806

Adjacent sequences: A318904 A318905 A318906 * A318908 A318909 A318910

Keyword

nonn

Author

Michel Lagneau, Sep 06 2018

Status

approved