A246436 Number of numbers 1,...,n not occurring in the Collatz trajectory starting with n.

0, 0, 0, 1, 1, 0, 2, 4, 2, 4, 4, 3, 6, 4, 8, 11, 8, 4, 8, 12, 15, 10, 14, 13, 11, 16, 17, 12, 15, 19, 21, 26, 16, 22, 26, 16, 19, 21, 21, 31, 28, 34, 23, 28, 31, 34, 34, 36, 29, 29, 33, 40, 43, 36, 40, 36, 33, 39, 37, 44, 47, 45, 48, 57, 42, 41, 45, 53, 56

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2014

Keywords

• nonn

Comments

a(n) = n - A159999(n).

Examples

			8-4-2-1: a(8) = #{3,5,6,7} = 4;
9-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1: a(9) = #{3,6} = 2;
10-5-16-8-4-2-1: a(10) = #{3,6,7,9} = 4;
11-34-17-52-26-13-40-20-10-5-16-8-4-2-1: a(11) = #{3,6,7,9} = 4;
12-6-3-10-5-16-8-4-2-1: a(12) = #{7,9,11} = 3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A159999, A220237, A070165.

Programs

Haskell

import Data.List ((\\), genericIndex)
a246436 n = length $ [1..n] \\ genericIndex a220237_tabf (n - 1)

Mathematica

Table[Length[Complement[Range[n],NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]]],{n,70}] (* Harvey P. Dale, May 27 2018 *)