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Search: id:A078418
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| A078418 |
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Numbers n such that h(n) = h(n-1) + h(n-2), 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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| 6, 22, 97, 108, 114, 495, 559, 2972, 3092, 3124, 3147, 3154, 3329, 3367, 3483, 3643, 3711, 3748, 3756, 3982, 4009, 4767, 17435, 17782, 17796, 17863, 17892, 17897, 18079, 18139, 18422, 18580, 18644, 18688, 18784, 18804, 18952, 19739, 19868
(list; graph; listen)
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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, 20, 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; 20, 10, 5, 16, 8, 4, 2, 1. Hence h(22) = 16 = 8 + 8 = h(21) + h(20) 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[3, 19900], h[ # ]==h[ #-1]+h[ #-2]&]
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CROSSREFS
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Cf. A078419, A078420.
Sequence in context: A003699 A047124 A046365 this_sequence A100300 A027296 A151495
Adjacent sequences: A078415 A078416 A078417 this_sequence A078419 A078420 A078421
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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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