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Search: id:A122563
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| A122563 |
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Start at 2n+1, iterate the map x -> A102421(x); sequence gives the number of iterations to resulting cycle. |
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1
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| 0, 2, 1, 1, 2, 3, 2, 1, 0, 0, 1, 3, 2, 2, 1, 6, 3, 5, 2, 4, 4, 0, 3, 3, 8, 8, 2, 7, 1, 4, 1, 3, 6, 3, 1, 2, 5, 11, 1, 4, 10, 7, 1, 9, 3, 9, 3, 9, 0, 8, 2, 2, 5, 8, 0, 7, 7, 7, 1, 4, 1, 2, 6, 6, 6, 9, 3, 1, 2, 5, 5, 5, 5, 8, 2, 2, 1, 10, 4, 16, 4, 4, 4, 4, 10, 6, 1, 9, 3, 15, 3, 3, 3, 6, 3, 3, 3, 8, 8, 2, 8, 14
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OFFSET
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0,2
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COMMENT
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Iteration: multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.
When a(x) is iterated, what are the limit cycles? Are there any besides {1} and {17 -> 19 -> 43 -> 97 -> 109 -> 61}?
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MATHEMATICA
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nextx[x_Integer] := Block[{a = x}, a = 3a + 1; While[EvenQ@a, a /= 2]; a = 3a - 1; While[EvenQ@a, a /= 2]; a]; f[n_] := Length@ NestWhileList[nextx, n, ! MemberQ[{1, 17, 19, 43, 97, 109}, # ] &] - 1; Table[ f[2n + 1], {n, 0, 101}]
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CROSSREFS
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Cf. A102421, A102423.
Adjacent sequences: A122560 A122561 A122562 this_sequence A122564 A122565 A122566
Sequence in context: A029254 A063740 A072782 this_sequence A080345 A004737 A014600
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 20 2006
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