A277367 -id:A277367 - cp's OEIS frontend

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

Michel Lagneau, Sep 06 2018

nonn

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), ...

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

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

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

cp's OEIS Frontend

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

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