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.

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

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

Table of n, a(n) for n=1..74.

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

Adjacent sequences: A307698 A307699 A307700 * A307702 A307703 A307704

Keyword

nonn,frac

Author

Andres Cicuttin, Apr 22 2019

Status

approved