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

1,2

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

Mathematica

coll[n_]:=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; Select[Range[101], Complement[Divisors[#], coll[#]]=={}&] (* Jayanta Basu, May 27 2013 *)

Prog

(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..]

Crossrefs

Cf. A027750, A070165, A006370, A207675 (complement), A000079 and A000040 are subsequences.

Sequence in context: A331914 A324935 A328369 * A162722 A123345 A093641

Adjacent sequences: A207671 A207672 A207673 * A207675 A207676 A207677

Keyword

nonn

Author

Reinhard Zumkeller, Feb 20 2012

Status

approved