%I A078419
%S A078419 2,5,22,495,559,2972,3092,3124,3147,3153,3184,3367,3711,3748,3857,3921,
%T A078419 3982,4450,4767,17019,17708,17769,17771,17782,17796,17825,17835,17857,
%U A078419 17863,17892,18079,18082,18139,18298,18422,18580,18644,18688,18784
%N A078419 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.)
%C A078419 Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.
%e A078419 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.
%t A078419 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[ # ]&]
%Y A078419 Cf. A078418, A078420.
%Y A078419 Sequence in context: A137069 A050994 A034384 this_sequence A070281 A019368 
               A141171
%Y A078419 Adjacent sequences: A078416 A078417 A078418 this_sequence A078420 A078421 
               A078422
%K A078419 nonn
%O A078419 1,1
%A A078419 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 29 2002
%E A078419 Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 30 2002