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A232711
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Conjectured list of positive numbers n such that the Collatz-like map T: if x odd, x -> 5*x+1 and if x even, x -> x/2, when started at n, eventually reaches 1.
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5
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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 n such that the Collatz-like map T: if x odd, x -> 5*x+1 and if x even, x -> x/2, when started at n, eventually reaches 1".
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LINKS
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EXAMPLE
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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 member.
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MATHEMATICA
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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)
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PROG
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(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)
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CROSSREFS
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Cf. A070165 (usual Collatz iteration).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Entry revised (corrected definition, added warnings to programs, deleted b-file) by N. J. A. Sloane, Jan 23 2016
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STATUS
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approved
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