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%I #5 May 10 2013 12:45:34
%S 2,2,3,3,5,7,11,17,31,53,95,173,317,587,1097,2049,3857,7287,13799,
%T 26217
%N Number of different cycles computed with the generalized 3x+1 problem using C=2, B=Cn+m, A=C^m.
%H J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html">The 3x+1 problem and its generalizations</a>, Amer. Math. Monthly, 92 (1985), 3-23.
%F 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.
%F a(n) = A000016(n)+1. - _Vladeta Jovovic_, Feb 14 2006
%e a(9)=59
%Y A008965 is the same sequence as this with A = -C^m.
%K nonn
%O 1,1
%A Peter Lengler (PeterLengler(AT)t-online.de), Jul 20 2004
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