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Numbers such that not all divisors occur in their Collatz trajectories.
3

%I #19 Oct 15 2018 18:57:35

%S 9,15,18,21,27,30,33,35,36,39,42,45,51,54,55,57,60,63,66,69,70,72,75,

%T 77,78,81,84,85,87,90,91,93,95,96,99,102,105,108,110,111,114,115,117,

%U 119,120,121,123,125,126,129,132,133,135,138,140,141,143,144,145

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

%H Reinhard Zumkeller, <a href="/A207675/b207675.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

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

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

%o (Haskell)

%o import Data.List (intersect)

%o a207675 n = a207675_list !! (n-1)

%o a207675_list = filter

%o (\x -> a027750_row x `intersect` a070165_row x /= a027750_row x) [1..]

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 20 2012