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A246436 Number of numbers 1,...,n not occurring in the Collatz trajectory starting with n. 2

%I #6 May 27 2018 14:23:02

%S 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,

%T 19,21,26,16,22,26,16,19,21,21,31,28,34,23,28,31,34,34,36,29,29,33,40,

%U 43,36,40,36,33,39,37,44,47,45,48,57,42,41,45,53,56

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

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

%H Reinhard Zumkeller, <a href="/A246436/b246436.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e 8-4-2-1: a(8) = #{3,5,6,7} = 4;

%e 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;

%e 10-5-16-8-4-2-1: a(10) = #{3,6,7,9} = 4;

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

%e 12-6-3-10-5-16-8-4-2-1: a(12) = #{7,9,11} = 3.

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

%o (Haskell)

%o import Data.List ((\\), genericIndex)

%o a246436 n = length $ [1..n] \\ genericIndex a220237_tabf (n - 1)

%Y Cf. A159999, A220237, A070165.

%K nonn

%O 1,7

%A _Reinhard Zumkeller_, Sep 01 2014

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Last modified September 14 06:54 EDT 2024. Contains 375920 sequences. (Running on oeis4.)