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A006460 Image of n after 3k iterates of '3x+1' map (k large).

%I A006460 M0304 #32 Aug 08 2022 15:54:08
%S A006460 1,2,2,4,4,4,2,1,2,1,4,1,1,4,4,2,1,4,4,2,2,1,1,2,4,2,1,1,1,1,2,4,4,2,
%T A006460 2,1,1,1,2,4,2,4,4,2,2,2,4,4,1,1,1,4,4,2,2,2,4,2,4,2,2,4,4,1,1,1,1,4,
%U A006460 4,4,1,2,2,2,4,2,2,4,4,1,2,4,4,1,1,1,1,4,1,4,4,4,4,1,1,1,2,2,2,2,2,2,1,1,4
%N A006460 Image of n after 3k iterates of '3x+1' map (k large).
%D A006460 R. K. Guy, Unsolved Problems in Number Theory, E16.
%D A006460 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006460 Reinhard Zumkeller, <a href="/A006460/b006460.txt">Table of n, a(n) for n = 1..10000</a>
%H A006460 M. Elia, <a href="/A006460/a006460.pdf">Letter to N. J. A. Sloane, Jun. 1981</a>
%H A006460 J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html">The 3x+1 problem and its generalizations</a>, Amer. Math. Monthly, 92 (1985), 3-23.
%H A006460 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A006460 For n > 2: a(n) = 4 if L = 0, otherwise L, where L = A139399(n) mod 3. - _Reinhard Zumkeller_, Nov 16 2013
%t A006460 f[n_] := If[EvenQ[n], n/2, 3 n + 1];
%t A006460 a[n_] := With[{ff = NestWhileList[f, n, {#1, #2, #3} != {4, 2, 1}&, 3]}, ff[[Switch[Mod[Length[ff], 3], 0, -3, 1, -1, 2, -2]]]];
%t A006460 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 08 2022 *)
%o A006460 (Haskell)
%o A006460 a006460 = f 0 where
%o A006460    f k x | mod k 3 == 0 && x `elem` [1, 2, 4] = x
%o A006460          | otherwise                          = f (k+1) (a006370 x)
%o A006460 -- _Reinhard Zumkeller_, Nov 16 2013
%Y A006460 Cf. A006370, A076052 (partial sums), A139399.
%K A006460 nonn,nice
%O A006460 1,2
%A A006460 _N. J. A. Sloane_
%E A006460 More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001