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%I #46 Jun 25 2024 23:44:03
%S 1,2,3,4,6,8,12,15,16,19,24,30,32,38,48,51,60,64,65,76,96,97,102,120,
%T 128,130,137,152,155,163,175,192,194,204,219,240,243,256,260,274,304,
%U 307,310,326,343,350,384,388,397,408,417,429,438,480,486,491,512
%N Conjectured list of numbers whose trajectory under the '5x+1' map eventually reaches 1.
%C 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
%C It appears that most numbers diverge, but nothing is known for certain.
%C 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".
%H Dmitry Kamenetsky, <a href="/A232711/b232711.txt">Table of n, a(n) for n = 1..1000</a>
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/px+1.html.html">The px+1 problem</a>.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 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.
%t 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)
%o (JavaScript)
%o for (i=1;i<2000;i++) {
%o c=0;
%o n=i;
%o while (n>1) {c++;if (n%2==0) n/=2; else n=5*n+1;if (c>100) break;}
%o if (c<101) document.write(i+", ");
%o } (Warning: bad program - will not find all the terms. - _N. J. A. Sloane_, Jan 23 2016)
%Y See A267969, A267970 for other trajectories under this map T.
%Y Cf. A057688, A133419.
%Y Cf. A070165 (usual Collatz iteration).
%K nonn
%O 1,2
%A _Jon Perry_, Nov 28 2013
%E Entry revised (corrected definition, added warnings to programs, deleted b-file) by _N. J. A. Sloane_, Jan 23 2016
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