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A075256
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List of pairs of numbers (a < b) in the sequence {a,b}-> {Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]} with k=3 and the first pair {a=1,b=2}.
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3
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1, 2, 1, 3, 2, 3, 1, 6, 3, 5, 2, 9, 6, 7, 1, 18, 3, 17, 9, 14, 5, 27, 15, 22, 7, 45, 21, 38, 17, 63, 46, 51, 5, 138, 15, 133, 45, 118, 73, 135, 62, 219, 157, 186, 29, 471, 87, 442, 261, 355, 94, 783, 282, 689, 407, 846, 439, 1221, 782, 1317, 535, 2346, 1605, 1811, 206
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OFFSET
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1,2
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COMMENTS
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Take any pair {a,b}. Each next pair is get by the rule {a,b} -> Sort[{Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]]. Here k=3 and the first {a,b}={1,2}. For k = 2 there is a fixed point {a,b=2a}. For k > 2, are there any limits or cycles of the sequence {for some initial pair {a,b}?
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LINKS
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Table of n, a(n) for n=1..65.
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FORMULA
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x(n+1) = Min[{Max[{x(n), y(n)}]-Min[{x(n), y(n)}], k*Min[{x(n), y(n)}]}];
y(n+1) = Max[{Max[{x(n), y(n)}]-Min[{x(n), y(n)}], k*Min[{x(n), y(n)}]}].
x(n) = A075257(n) = a(2n-1), y(n) = A075258(n) = A075256(2n).
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EXAMPLE
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3rd pair is {2,3} because 2nd pair is {1,3}, Max[{a,b}]-Min[{a,b}] = 3 - 1 = 2, 3*Min[{a,b}] = 3*1 = 3.
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MATHEMATICA
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ss=Table[0, {j, 100}]; s=ss[[1]]={1, 2}; Do[ss[[i]]=Sort[{Max[s]-Min[s], 3*Min[s]}]; s=ss[[i]], {i, 2, 100}]; Flatten[ss]
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CROSSREFS
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Cf. A075257, A075258.
Sequence in context: A060162 A026730 A318691 * A334523 A001480 A308117
Adjacent sequences: A075253 A075254 A075255 * A075257 A075258 A075259
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KEYWORD
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nonn,tabf
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AUTHOR
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Zak Seidov, Sep 10 2002
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STATUS
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approved
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