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A129304
Numbers whose Collatz trajectory does not have the same number of halving steps and the same number of tripling steps as that of any smaller number.
3
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 20, 22, 24, 25, 27, 28, 31, 32, 33, 34, 36, 39, 40, 41, 43, 44, 47, 48, 49, 54, 56, 57, 62, 64, 65, 68, 71, 72, 73, 78, 80, 82, 86, 88, 91, 94, 96, 97, 98, 103, 105, 107, 108, 111, 112, 114, 121, 123, 124, 128, 129, 130
OFFSET
1,2
COMMENTS
Note that if k is in this sequence, then 2k is also. The plot shows a very narrow triangle of the possible halving/tripling pairs. As n increases, the width of the triangle grows on its right edge.
EXAMPLE
For each integer k, let the ordered pair (h,t) give the numbers of halving and tripling steps in the Collatz trajectory of k. The pairs for k = 1..16 are (0,0), (1,0), (5,2), (2,0), (4,1), (6,2), (11,5), (3,0), (13,6), (5,1), (10,4), (7,2), (7,2), (12,5), (12,5), (4,0). Thus 13 and 15 are not in this sequence because their pairs are the same as for 12 and 14, respectively.
MATHEMATICA
Collatz[n_] := Module[{c1=0, c2=0, m=n}, While[m>1, If[EvenQ[m], c1++; m=m/2, c2++; m=3m+1]]; {c1, c2}]; s={}; t={}; n=0; While[Length[t]<100, n++; c=Collatz[n]; If[ !MemberQ[s, c], AppendTo[s, c]; AppendTo[t, n]]]; t
CROSSREFS
Cf. A006666 (number of halving steps), A006667 (number of tripling steps).
Sequence in context: A066255 A330236 A302593 * A337149 A294358 A262358
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 09 2007
STATUS
approved