

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
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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), 323.


FORMULA

Generalize the 3x+1Problem 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: A133277 A133276 A055501 * A241507 A243927 A102330
Adjacent sequences: A096007 A096008 A096009 * A096011 A096012 A096013


KEYWORD

nonn


AUTHOR

Peter Lengler (PeterLengler(AT)tonline.de), Jul 20 2004


STATUS

approved



