A037084 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.

5, 7, 9, 10, 13, 14, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 61, 62, 63, 66, 67, 68, 70, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 89, 90, 91, 92, 93, 94, 98, 99, 100, 102

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

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

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

Complement (in N*) of A039500 ; union of A039501 and A039502 (conjectured). - M. F. Hasler, Nov 26 2007

Equivalent to the Collatz ('3n+1') problem for negative integers. - Dmitry Kamenetsky, Jan 12 2017

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001281, A039500-A039505.

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

Programs

Mathematica

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

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

Extensions

More terms from Christian G. Bower, Feb 15 1999

Edited by M. F. Hasler, Nov 26 2007