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".
LINKS
Dmitry Kamenetsky, Table of n, a(n) for n = 1..1000
Tomás Oliveira e Silva, The px+1 problem.
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
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