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

1,7

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A159999, A220237, A070165.

Sequence in context: A184186 A004020 A363290 * A143235 A069465 A047947

Adjacent sequences: A246433 A246434 A246435 * A246437 A246438 A246439

Keyword

nonn

Author

Reinhard Zumkeller, Sep 01 2014

Status

approved