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A226662
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Smallest positive integer k (or 0 if no such k) with conjecturally exactly n primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.
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2
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1, 11, 23, 29, 5, 247, 47, 229, 13, 361, 359, 517, 481, 1669, 485, 1843, 295, 269, 233, 355, 2509, 1399, 431, 943, 1991, 4715, 7469, 3323, 1753, 2777, 781, 2347, 1201, 4741, 9233, 12607, 6559, 6721, 4879, 2359, 5531, 1805, 11773, 11113, 6755, 8861, 5897, 30079
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OFFSET
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1,2
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COMMENTS
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A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
The 3x+k function T_k is defined by T_k(x) = x/2 if x is even, (3x+k)/2 if x is odd, where k is odd.
For primitive cycles, GCD(k,6)=1.
Belaga and Mignotte (2000, p.19) conjectured that the number of primitive cycles attains all positive integer values.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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