A207675 Numbers such that not all divisors occur in their Collatz trajectories.

9, 15, 18, 21, 27, 30, 33, 35, 36, 39, 42, 45, 51, 54, 55, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 96, 99, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 125, 126, 129, 132, 133, 135, 138, 140, 141, 143, 144, 145

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2012

Keywords

• nonn

Examples

			3 is a divisor of 9, not occurring in A033479 - therefore 9 is a term.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A027750, A070165, A006370, A207674 (complement).

Programs

Haskell

import Data.List (intersect)
a207675 n = a207675_list !! (n-1)
a207675_list = filter
   (\x -> a027750_row x `intersect` a070165_row x /= a027750_row x) [1..]

Mathematica

coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Select[Range[145],Complement[Divisors[#],coll[#]]!={}&] (* Jayanta Basu, May 27 2013 *)