A216022 Largest number m such that the Collatz trajectory starting at n contains all numbers not greater than m.

1, 2, 5, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2012

Keywords

• nonn

Comments

a(n) <= 6; a(A007283(n)) = 6;

a(n) > 1 for n > 1; a(n) <> 3; a(n) <> 4; a(n) <> 5 for n > 3;

a(n) = A216059(n) - 1.

In the first 100000 terms, there are only 16 terms greater than 2, all of which but one are equal to 6. - Harvey P. Dale, Nov 29 2019

Examples

			n = 3->10->5->16->8->4->2->1 => {1_2_3_4_5 8 10 16}, a(3) = 5;
n = 4->2->1 => {1_2 4}, a(4) = 2;
n = 5->16->8->4->2->1 => {1_2 4 5 8 16}, a(5) = 2;
n = 6->3->10->5->16->8->4->2->1 => {1_2_3_4_5_6 8 10 16}, a(6) = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A070165.

Programs

Haskell

import Data.List (sort)
a216022 = length .
   takeWhile (== 0) . zipWith (-) [1..] . sort . a070165_row

Mathematica

scoll[n_]:=Sort[NestWhileList[If[EvenQ[#],#/2,3#+1] &,n,#>1 &]]; Join[{1,2},Table[i=1; While[scoll[n][[i]]==i,i++]; i-1,{n,3,86}]] (* Jayanta Basu, May 27 2013 *)
Join[{1,2},Flatten[Table[Position[Differences[Sort[ NestWhileList[ If[ EvenQ[#],#/2,3#+1]&,n,#>1&]]], ?(#>1&),1,1],{n,90}]]] (* _Harvey P. Dale, Nov 29 2019 *)