The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A020653

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A020653

Denominators in a certain bijection from positive integers to positive rationals.
(history; published version)

#53 by Michael De Vlieger at Tue May 14 09:13:52 EDT 2024

STATUS

reviewed

approved

#52 by Michel Marcus at Tue May 14 07:03:05 EDT 2024

STATUS

proposed

reviewed

#51 by Ruud H.G. van Tol at Tue May 14 06:17:19 EDT 2024

STATUS

editing

proposed

#50 by Ruud H.G. van Tol at Tue May 14 06:16:53 EDT 2024

PROG

(PARI) a(n) = my(s=0, k=1, j=1); while(s<n, s+=eulerphi(k++)); s-=eulerphi(k); while(s<n, if(1==gcd(j, k), s++); j++); k+1-j; \\ Ruud H.G. van Tol, May 14 2024

STATUS

approved

editing

#49 by N. J. A. Sloane at Thu Nov 25 09:03:59 EST 2021

STATUS

editing

approved

#48 by N. J. A. Sloane at Thu Nov 25 09:03:56 EST 2021

NAME

Denominators in one of the bijections a certain bijection from positive integers to positive rationals.

STATUS

approved

editing

#47 by N. J. A. Sloane at Thu Nov 25 09:02:48 EST 2021

STATUS

editing

approved

#46 by N. J. A. Sloane at Thu Nov 25 09:02:46 EST 2021

COMMENTS

Here, the canonical This bijection means to list lists the fractions p/q (in lowest terms) by increasing p+q, then by increasing p, cf. (see the example). The variant A038569 corresponds to a different "canonical the bijection", where each fraction p/q with p < q is followed by its reciprocal q/p. - M. F. Hasler, Oct 25 2021

STATUS

approved

editing

#45 by N. J. A. Sloane at Thu Nov 25 09:00:53 EST 2021

STATUS

editing

approved

#44 by N. J. A. Sloane at Thu Nov 25 09:00:50 EST 2021

NAME

Denominators in canonical bijection one of the bijections from positive integers to positive rationals.

EXTENSIONS

Definition clarified by N. J. A. Sloane, Nov 25 2021