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Search: id:A129304
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| A129304 |
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Numbers n such that the Collatz iteration requires a different number of halving and tripling steps than any previous number. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Note that if n is in this sequence, then 2n 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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..2000
T. D. Noe, Plot of the 2000 possible halving/tripling pairs for n <= 7540196
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EXAMPLE
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Each any n, let the ordered pair (h,t) give the number of halving and tripling steps in the Collatz iteration. The pairs for the first 16 numbers 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.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A006666 (number of halving steps), A006667 (number of tripling steps).
Sequence in context: A028828 A058226 A066255 this_sequence A032962 A032519 A008730
Adjacent sequences: A129301 A129302 A129303 this_sequence A129305 A129306 A129307
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Apr 09 2007
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