A213330 Minimum deviation from n in Collatz trajectory of n.

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

Offset: 1

Author

Jayanta Basu, Mar 03 2013

Keywords

• nonn

Comments

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

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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