This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318907 #13 Jan 08 2025 13:01:49
%S A318907 5,6,10,17,20,21,24,26,40,42,44,45,46,80,84,85,96,104,106,112,113,116,
%T A318907 117,120,122,136,138,140,141,150,151,159,160,168,170,283,288,296,298,
%U A318907 304,308,309,320,321,324,325,326,331,336,340,341,377,384,416,424,426
%N A318907 Numbers m such that A006666(m)/A006667(m) is an integer.
%C A318907 A006666 and A006667 are respectively the number of halving and tripling steps in the '3x+1' problem.
%C A318907 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, ...
%C A318907 The numbers of the form (4^k - 1)/3 for k > 1 (A002450) are in the sequence.
%C A318907 We observe subsets of consecutive numbers: (5, 6), (20, 21), (44, 45, 46), (84, 85), (112, 113), ...
%e A318907 17 is in the sequence because A006666(17)/A006667(17) = 9/3 = 3 is an integer.
%t A318907 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
%Y A318907 Cf. A002450, A006666, A006667, A277367, A281938.
%K A318907 nonn
%O A318907 1,1
%A A318907 _Michel Lagneau_, Sep 06 2018