login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307701 Denominator of the irreducible fractions of the form x/y, with x,y primes and x < y, sorted according to increasing k, with k = x + y. Fractions with same k are sorted in order of increasing denominator. 1
3, 5, 5, 7, 7, 7, 11, 11, 13, 11, 13, 11, 13, 17, 13, 17, 19, 17, 19, 13, 17, 19, 23, 19, 23, 17, 23, 17, 19, 23, 29, 19, 29, 31, 23, 29, 31, 19, 23, 29, 31, 31, 37, 23, 29, 37, 23, 29, 31, 37, 41, 31, 37, 41, 43, 29, 41, 43, 29, 31, 37, 41, 43, 47, 31, 37, 43, 47, 29, 41, 47, 31, 37, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The parameter k is the Manhattan distance of the corresponding points to the origin in the "denominator, numerator" representation space.
This sequence (denominators) and A306894 (numerators) are respectively subsequences of A280315 and A280073, when both A280315(x) and A280073(x) are primes.
LINKS
EXAMPLE
The first fractions are 2/3, 2/5, 3/5, 2/7, 3/7, ... with increasing k = 5,7,8,9,10,... respectively, then first terms are the corresponding denominators, 3,5,5,7,7,...
MATHEMATICA
nmax=125;
(* fracs are fractions represented in the triangle with vertices (2, 3), (2, prime(nmax)) and (prime(nmax), prime(nmax)) *)
fracs=Sort@Flatten@Table[Prime[a]/Prime[b], {b, 2, nmax}, {a, 1, b-1}];
(* Sorting generated fractions according to increasing Manhattan distance first, and then by increasing denominator *)
fracsorted=SortBy[fracs, {Numerator@#+Denominator@#&, Denominator@#&}];
nmaxlimit=Floor[(1/6)*nmax^2]; (* Safe limit for a correctly sorted sequence since asymptotically half of the generated fractions can be properly sorted according to Manhattan distance *)
Take[Denominator@fracsorted, nmaxlimit]
CROSSREFS
Cf. A306894 (numerators), A279782, A279783, A280073, A280315.
Sequence in context: A360635 A126611 A164019 * A103332 A195796 A279944
KEYWORD
nonn,frac
AUTHOR
Andres Cicuttin, Apr 22 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)