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A177729
Positive integers which do not appear in a Collatz sequence starting from a smaller positive integer.
10
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
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
KEYWORD
nonn
AUTHOR
Raul D. Miller, May 12 2010
STATUS
approved