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

1,1

Links

Table of n, a(n) for n=1..20.

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

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

Example

a(9)=59

Crossrefs

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

Sequence in context: A133276 A354485 A055501 * A241507 A243927 A102330

Adjacent sequences: A096007 A096008 A096009 * A096011 A096012 A096013

Keyword

nonn

Author

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

Status

approved