A232711 Conjectured list of numbers whose trajectory under the '5x+1' map eventually reaches 1.

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

Author

Jon Perry, Nov 28 2013

Keywords

• nonn

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".

Examples

			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.
		

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..1000
• Tomás Oliveira e Silva, The px+1 problem.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

See A267969, A267970 for other trajectories under this map T.

Cf. A057688, A133419.

Cf. A070165 (usual Collatz iteration).

Programs

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)

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)

Extensions

Entry revised (corrected definition, added warnings to programs, deleted b-file) by N. J. A. Sloane, Jan 23 2016