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Least odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.
4

%I #7 Mar 04 2013 15:32:34

%S 1,0,0,3,0,13,7,9,19,25,33,43,39,79,105,135,123,169,159,295,283,111,

%T 223,297,175,103,91,121,31,27,55,73,97,129,171,231,313,411,543,327,

%U 649,859,763,1017,1351,1215,703,937,871,1161,2223,3097,2631,3567,3175,4233

%N Least odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.

%H T. D. Noe, <a href="/A222754/b222754.txt">Table of n, a(n) for n = 0..100</a>

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 51; t = Table[0, {nn}]; n = -1; While[Min[Drop[t, 5]] == 0, n = n + 2; c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1 && t[[diff + 2]] == 0, t[[diff + 2]] = n]]; t

%Y Cf. A222752, A222753, A222755.

%K nonn

%O 0,4

%A _T. D. Noe_, Mar 04 2013