

A078418


Numbers n such that h(n) = h(n1) + h(n2), 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.)


2



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
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OFFSET

1,1


COMMENTS

Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.


LINKS



EXAMPLE

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.


MATHEMATICA

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]&]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



