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A222617
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Number of integers k < n whose Collatz (3x+1) trajectory contains n.
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1
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0, 0, 0, 1, 1, 0, 0, 4, 0, 4, 2, 0, 3, 1, 0, 11, 4, 0, 0, 9, 0, 5, 1, 0, 0, 9, 0, 2, 2, 0, 1, 1, 0, 11, 5, 0, 0, 2, 0, 25, 1, 0, 0, 6, 0, 5, 3, 0, 1, 1, 0, 23, 9, 0, 0, 3, 0, 7, 1, 0, 6, 3, 0, 2, 2, 0, 2, 1, 0, 14, 7, 0, 0, 4, 0, 7, 1, 0, 0, 19, 0, 2, 2, 0, 1
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OFFSET
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1,8
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COMMENTS
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It is assumed that Collatz trajectory ends at 1.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E16.
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LINKS
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EXAMPLE
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a(8)=4, since 8 appears in Collatz trajectories of n < 8; similarly a(9)=0 since 9 does not appear in Collatz trajectories n < 9.
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MATHEMATICA
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Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 100; t = Table[Collatz[n], {n, nn}]; Table[r = 0; Do[If[MemberQ[t[[i]], k], r++], {i, k - 1}]; r, {k, nn}] (* T. D. Noe, Feb 26 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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