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 A318907 Numbers m such that A006666(m)/A006667(m) is an integer. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)