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A221474
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Number of families of numbers requiring n iterations of the Collatz (3x+1) function to reach 1.
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1
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1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 3, 3, 4, 4, 5, 4, 6, 5, 6, 5, 7, 6, 7, 7, 8, 7, 9, 8, 9, 9, 10, 10, 11, 10, 11, 11, 12, 11, 13, 12, 13, 13, 14, 14, 15, 14, 16, 15, 16, 16, 17, 17, 18, 17, 18, 18, 19, 19, 20, 19, 21, 20, 22, 21, 23, 22, 24
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OFFSET
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0,8
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COMMENTS
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Looking at the graph of A221473, it is apparent that the numbers requiring n iterations clump into families.
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LINKS
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MATHEMATICA
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nn = 41; s = {1}; t = Join[s, Table[s = Union[2 s, (Select[s, Mod[#, 3] == 1 && OddQ[(# - 1)/3] && (# - 1)/3 > 1 &] - 1)/3]; s, {n, nn-1}]]; t2 = Join[{{t[[1]]}}, Table[Select[t[[i]], OddQ], {i, 2, nn}]]; Table[t3 = t2[[n]]; If[Length[t3] <= 1, Length[t3], s = Round[Rest[t3]/Most[t3]]; Length[Select[s, # > 1 &]] + 1], {n, nn}]
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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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