A177729 Positive integers which do not appear in a Collatz sequence starting from a smaller positive integer.

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, 55, 57, 60, 63, 66, 69, 72, 73, 75, 78, 79, 81, 84, 87, 90, 93, 96, 97, 99, 102, 105, 108, 109, 111, 114, 115, 117, 120, 123, 126, 127, 129, 132, 133, 135, 138, 141

Offset: 1

Author

Raul D. Miller, May 12 2010

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• David Eisenbud and Brady Haran, UNCRACKABLE? The Collatz Conjecture, Numberphile Video, 2016.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

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

Programs

Haskell

a177729 = head . a192719_row  -- Reinhard Zumkeller, Jan 03 2013

Mathematica

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 *)

Formula

a(n) = A192719(n,1), see also A220263. - Reinhard Zumkeller, Jan 03 2013