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A232711
Conjectured list of numbers whose trajectory under the '5x+1' map eventually reaches 1.
6
1, 2, 3, 4, 6, 8, 12, 15, 16, 19, 24, 30, 32, 38, 48, 51, 60, 64, 65, 76, 96, 97, 102, 120, 128, 130, 137, 152, 155, 163, 175, 192, 194, 204, 219, 240, 243, 256, 260, 274, 304, 307, 310, 326, 343, 350, 384, 388, 397, 408, 417, 429, 438, 480, 486, 491, 512
OFFSET
1,2
COMMENTS
This is conjectural in that there is no known proof that 7, 9, 11, etc. (see A267970) do not eventually cycle. - N. J. A. Sloane, Jan 23 2016
It appears that most numbers diverge, but nothing is known for certain.
Note that the computer programs do not actually calculate a complete list of "numbers k such that the Collatz-like map T: if x odd, x -> 5*x+1 and if x even, x -> x/2, when started at k, eventually reaches 1".
EXAMPLE
Beginning with 15 we get the trajectory 15, 76, 38, 19, 96, 48, 24, 12, 6, 3, 16, 8, 4, 2, 1, so 15 is a term.
MATHEMATICA
cli=Compile[{{n, _Integer}}, If[OddQ[n], 5n+1, n/2]//Round, RuntimeAttributes->{Listable}, Parallelization->True]; okQ[n_]:=Length[NestWhileList[cli, n, #>1&, 1, 200]]<200; Select[Range[550], okQ] (* Harvey P. Dale, May 28 2014 *) (Warning: bad program - will not find all the terms. - N. J. A. Sloane, Jan 23 2016)
PROG
(JavaScript)
for (i=1; i<2000; i++) {
c=0;
n=i;
while (n>1) {c++; if (n%2==0) n/=2; else n=5*n+1; if (c>100) break; }
if (c<101) document.write(i+", ");
} (Warning: bad program - will not find all the terms. - N. J. A. Sloane, Jan 23 2016)
CROSSREFS
See A267969, A267970 for other trajectories under this map T.
Cf. A070165 (usual Collatz iteration).
Sequence in context: A336506 A336508 A260653 * A178751 A309353 A081029
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 28 2013
EXTENSIONS
Entry revised (corrected definition, added warnings to programs, deleted b-file) by N. J. A. Sloane, Jan 23 2016
STATUS
approved