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A096010
Number of different cycles computed with the generalized 3x+1 problem using C=2, B=Cn+m, A=C^m.
0
2, 2, 3, 3, 5, 7, 11, 17, 31, 53, 95, 173, 317, 587, 1097, 2049, 3857, 7287, 13799, 26217
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
Peter Lengler (PeterLengler(AT)t-online.de), Jul 20 2004
STATUS
approved