

A177729


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


8



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
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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 nonstandard 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. AdamsWatters, 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, 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, n1}], 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: A061951 A153348 A246647 * A049993 A167793 A262932
Adjacent sequences: A177726 A177727 A177728 * A177730 A177731 A177732


KEYWORD

nonn


AUTHOR

Raul D. Miller, May 12 2010


STATUS

approved



