|
|
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
(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
|
|
|
FORMULA
|
|
|
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)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|