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A206297
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Position of n in the canonical bijection from the positive integers to the positive rational numbers.
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4
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1, 3, 5, 9, 13, 21, 25, 37, 45, 57, 65, 85, 93, 117, 129, 145, 161, 193, 205, 241, 257, 281, 301, 345, 361, 401, 425, 461, 485, 541, 557, 617, 649, 689, 721, 769, 793, 865, 901, 949, 981, 1061, 1085, 1169, 1209, 1257, 1301, 1393, 1425, 1509, 1549
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OFFSET
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1,2
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COMMENTS
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The canonical bijection from the positive integers to the positive rational numbers is given by A038568(n)/A038569(n).
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LINKS
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EXAMPLE
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The canonical bijection starts with 1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, 1/5, 5/1, so that this sequence starts with 1,3,5,9,13 and A206350 starts with 1,2,4,8,12.
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MATHEMATICA
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a[n_] := Module[{s = 1, k = 2, j = 1},
While[s <= n, s = s + 2*EulerPhi[k]; k = k + 1];
s = s - 2*EulerPhi[k - 1];
While[s <= n, If[GCD[j, k - 1] =
= 1, s = s + 2]; j = j + 1];
If[s > n + 1, j - 1, k - 1]];
t = Table[a[n], {n, 0, 3000}]; (* A038568 *)
ReplacePart[1 + Flatten[Position[t, 1]], 1, 1]
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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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