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Minimum deviation from n in Collatz trajectory of n.
1

%I #15 Oct 13 2022 22:31:41

%S 0,1,1,2,1,1,1,4,1,2,1,2,3,1,1,8,1,1,1,4,5,2,3,8,1,6,4,2,3,5,4,16,1,6,

%T 5,2,3,2,1,20,1,10,3,4,5,6,1,24,3,2,1,12,13,1,2,4,1,6,1,7,8,1,2,32,9,

%U 8,9,16,17,10,1,20,2,18,10,12,11,2,3,40,1,2

%N Minimum deviation from n in Collatz trajectory of n.

%C Assuming Collatz trajectory ends with 1 and also a(1)=0.

%H T. D. Noe, <a href="/A213330/b213330.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4)=2 because the number closest to 4 in Collatz trajectory of 4 is 2.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Join[{0}, Table[Min[Rest[Abs[Collatz[n] - n]]], {n, 2, 100}]]

%Y Cf. A070165, A355239 (indices of 1's).

%K nonn

%O 1,4

%A _Jayanta Basu_, Mar 03 2013