OFFSET
0,2
COMMENTS
First occurrence of n in A006667.
Except for a(1) = 5, all values are congruent {1, 3, 7} (mod 8). Reason: If n is 5 (mod 8) then the Collatz trajectory starting with m = (n - 1)/4 contains the same number of tripling steps, because n = 4m + 1 and the Collatz 3x + 1 step results in 3*(4m + 1) + 1 = 12m + 4 which gets reduced by halving to 3m + 1, without changing the number of tripling steps. - Ralf Stephan, Jun 19 2025
LINKS
T. D. Noe, Table of n, a(n) for n=0..300
Jeffrey R. Goodwin, The 3x+1 Problem and Integer Representations, Arxiv preprint arXiv:1504.03040 [math.NT], 2015.
Eric Weisstein's World of Mathematics, Collatz Problem
EXAMPLE
a(4)=11 because the Collatz sequence 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 is the first sequence containing 4 tripling steps.
MATHEMATICA
a[n_]:=Length[Select[NestWhileList[If[EvenQ[#], #/2, 3#+1] &, n, #>1 &], OddQ]]; Table[i=1; While[a[i]!=n, i=i+2]; i, {n, 58}] (* Jayanta Basu, May 27 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Mar 11 2004
STATUS
approved
