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A226623
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Irregular array read by rows in which row n lists the smallest elements, in ascending order, of conjecturally all primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k = A226630(n).
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9
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1, 5, 17, 19, 65, 73, 115, 2263, 2359, 2743, 2963, 3091, 3415, 3743, 4819, 113, 109, 95, 65, 989, 1153, 1165, 293, 511, 505, 625, 769, 211, 227, 251, 311, 1085, 2089, 7471, 10883, 13963, 15875, 16099, 1291, 1355, 1367, 1495, 1931, 2059, 2123, 2203, 2219, 2251
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OFFSET
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1,2
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COMMENTS
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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.
Lagarias (1990) called a T_k cycle primitive if its elements are all relatively prime to k or, equivalently, if its elements are not a common multiple of the elements of another cycle.
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LINKS
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EXAMPLE
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The irregular array starts:
(k=1) 1, 5, 17;
(k=11) 19;
(k=17) 65, 73;
(k=19) 115;
a(4)=19 is the smallest number in the 3x-11 cycle {19,23,29,38}.
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CROSSREFS
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The smallest starting value whose trajectory includes a(n) is A226627(n). The cycle associated with a(n) has length A226625(n) and A226626(n) odd elements of which A226624(n) is the largest
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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