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Positive integers not going to 1 under iterations of the map in A001281: n->3n-1 if n odd, n->n/2 if n even.
12

%I #25 Jun 13 2017 02:15:59

%S 5,7,9,10,13,14,17,18,19,20,21,23,25,26,27,28,31,33,34,35,36,37,38,40,

%T 41,42,45,46,47,49,50,51,52,54,55,56,61,62,63,66,67,68,70,72,73,74,75,

%U 76,80,81,82,83,84,89,90,91,92,93,94,98,99,100,102

%N Positive integers not going to 1 under iterations of the map in A001281: n->3n-1 if n odd, n->n/2 if n even.

%C Up to at least 100000000, every number reaches 1, 5 or 17.

%C Conjecture : for any x, the iterated process "x ->3x-1" if x is odd or "x ->x/2" if x is even leads to one of the following three cycles: (1, 2), (5, 14, 7, 20, 10), (41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82). - _Benoit Cloitre_, May 14 2002

%C Complement (in N*) of A039500 ; union of A039501 and A039502 (conjectured). - _M. F. Hasler_, Nov 26 2007

%C Equivalent to the Collatz ('3n+1') problem for negative integers. - _Dmitry Kamenetsky_, Jan 12 2017

%H Alois P. Heinz, <a href="/A037084/b037084.txt">Table of n, a(n) for n = 1..20000</a>

%e Iterations of f starting at 3 are 3,8,4,2,1 - thus 3 is not in the sequence.

%e Iterations starting at 5 are 5,14,7,20,10,5 -periodic and 1 is not among these values, so 5 is in the sequence.

%t colln[n_]:= NestWhile[If[EvenQ[#], #/2, 3#-1] &, n, FreeQ[{1, 5, 17}, #] &]; Select[Range[102], colln[#] != 1 &] (* _Jayanta Basu_, Jun 06 2013 *)

%o (PARI) A037084( end=999, n=0 /*starting value -1 */)={ for( i=n,end, n=i; while( n > 17 || n > 5 && n < 17, if( n%2, n=3*n-1, n>>=1)); if( n > 4, print1(i", ")))} \\ _M. F. Hasler_, Nov 26 2007

%Y Cf. A001281, A039500-A039505.

%Y Cf. A006370, A006577 (Collatz problem: 3n+1).

%K nonn,easy

%O 1,1

%A Robert W. Craigen (craigen(AT)fresno.edu)

%E More terms from _Christian G. Bower_, Feb 15 1999

%E Edited by _M. F. Hasler_, Nov 26 2007