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Search: id:A078419
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| A078419 |
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Numbers n such that h(n) = 2 h(n-1) where h(n) is the length of the sequence {n, f(n), f(f(n)), ...., 1} in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.) |
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3
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| 2, 5, 22, 495, 559, 2972, 3092, 3124, 3147, 3153, 3184, 3367, 3711, 3748, 3857, 3921, 3982, 4450, 4767, 17019, 17708, 17769, 17771, 17782, 17796, 17825, 17835, 17857, 17863, 17892, 18079, 18082, 18139, 18298, 18422, 18580, 18644, 18688, 18784
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OFFSET
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1,1
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COMMENT
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Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.
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EXAMPLE
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n, f(n), f(f(n)), ...., 1 for n = 22, 21, respectively, are: 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1; 21, 64, 32, 16, 8, 4, 2, 1. Hence h(22) = 16 = 2 * 8 = h(21) and 22 belongs to the sequence.
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MATHEMATICA
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f[n_] := If[EvenQ[n], n/2, 3n+1]; h[n_] := Module[{a, i}, i=n; a=1; While[i>1, a++; i=f[i]]; a]; Select[Range[2, 18800], 2h[ #-1]==h[ # ]&]
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CROSSREFS
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Cf. A078418, A078420.
Sequence in context: A137069 A050994 A034384 this_sequence A070281 A019368 A141171
Adjacent sequences: A078416 A078417 A078418 this_sequence A078420 A078421 A078422
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 29 2002
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 30 2002
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