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A206297 Position of n in the canonical bijection from the positive integers to the positive rational numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The canonical bijection from the positive integers to the positive rational numbers is given by A038568(n)/A038569(n).

Appears to be a variant of A049691. - R. J. Mathar, Feb 11 2012

It appears that a(n) = 2*A005728(n) - 1. - Chris Boyd, Mar 21 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

EXAMPLE

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.

MATHEMATICA

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]

(* A206297 *)

CROSSREFS

Cf. A038568, A038569, A206350.

Sequence in context: A076274 A058989 A049691 * A227565 A136252 A187212

Adjacent sequences:  A206294 A206295 A206296 * A206298 A206299 A206300

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling, Feb 06 2012

STATUS

approved

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Last modified December 17 16:25 EST 2017. Contains 296119 sequences.