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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 (list; graph; refs; listen; history; text; internal format)
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, 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: 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

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Last modified November 21 22:32 EST 2017. Contains 295054 sequences.