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

1,2

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

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A341257 A153348 A246647 * A049993 A167793 A262932

Adjacent sequences: A177726 A177727 A177728 * A177730 A177731 A177732

Keyword

nonn

Author

Raul D. Miller, May 12 2010

Status

approved