A207674 Numbers such that all divisors occur in their Collatz trajectories.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 25, 26, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 97, 98, 100, 101

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2012

Keywords

• nonn

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, A207675 (complement), A000079 and A000040 are subsequences.

Programs

Haskell

import Data.List (intersect)
a207674 n = a207674_list !! (n-1)
a207674_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[101],Complement[Divisors[#],coll[#]]=={}&] (* Jayanta Basu, May 27 2013 *)