A096010 Number of different cycles computed with the generalized 3x+1 problem using C=2, B=Cn+m, A=C^m.

2, 2, 3, 3, 5, 7, 11, 17, 31, 53, 95, 173, 317, 587, 1097, 2049, 3857, 7287, 13799, 26217

Offset: 1

Author

Peter Lengler (PeterLengler(AT)t-online.de), Jul 20 2004

Keywords

• nonn

Examples

			a(9)=59
		

Links

• J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.

Crossrefs

A008965 is the same sequence as this with A = -C^m.

Formula

Generalize the 3x+1-Problem from S:= S / 2 if S is even, S:= (S * 3) + 1 if S is odd to S:= S / C if C | S S:= (S * B) + A otherwise. For B=Cn+A, A=C^m the number of different cycles z are computed. Every S leads to a cycle, so it can be conjectured that the number of cycles is infinite. But the number of different cycles seems to be finite. It is conjectured that the last new cycle occurs at the starting number S = B. This was tested with A=1; B=3; C=2 up to S=100000000.

a(n) = A000016(n)+1. - Vladeta Jovovic, Feb 14 2006