%I #30 Jun 10 2018 19:48:26

%S 1,2,3,6,7,9,12,15,18,19,21,24,25,27,30,33,36,37,39,42,43,45,48,51,54,

%T 55,57,60,63,66,69,72,73,75,78,79,81,84,87,90,93,96,97,99,102,105,108,

%U 109,111,114,115,117,120,123,126,127,129,132,133,135,138,141

%N Positive integers which do not appear in a Collatz sequence starting from a smaller positive integer.

%C A variant of A061641, which is the main entry for this sequence.

%C The inclusion of 2 is apparently due to a non-standard definition of a Collatz sequence; A177729 assumes that the Collatz sequence ends when it reaches 1, whereas the standard definition includes the periodic 1,4,2,... from that point. The inclusion of 0 in A061641 is a bit odd, but is not actually wrong. One usually looks only at positive integers for Collatz sequences. - _Franklin T. Adams-Watters_, May 14 2010

%H Reinhard Zumkeller, <a href="/A177729/b177729.txt">Table of n, a(n) for n = 1..10000</a>

%H David Eisenbud and Brady Haran, <a href="https://www.youtube.com/watch?v=5mFpVDpKX70">UNCRACKABLE? The Collatz Conjecture</a>, Numberphile Video, 2016.

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

%F a(n) = A192719(n,1), see also A220263. - _Reinhard Zumkeller_, Jan 03 2013

%e Collatz 1: 1; Collatz 2: 2,1; Collatz 3: 3,10,5,16,8,4,2,1; Collatz 6: 6,3,10,...

%t coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; t={1}; Do[If[FreeQ[Union@@Table[coll[i],{i,n-1}],n],AppendTo[t,n]],{n,2,141}]; t (* _Jayanta Basu_, May 29 2013 *)

%o (Haskell)

%o a177729 = head . a192719_row -- _Reinhard Zumkeller_, Jan 03 2013

%Y Cf. A006577, A061641, A070167, A112695, A192719, A220263.

%K nonn

%O 1,2

%A _Raul D. Miller_, May 12 2010