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

1,2

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

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A006370, A070165.

Sequence in context: A065291 A065267 A273990 * A100955 A049413 A300691

Adjacent sequences: A216019 A216020 A216021 * A216023 A216024 A216025

Keyword

nonn

Author

Reinhard Zumkeller, Sep 01 2012

Status

approved