cp's OEIS Frontend

A279067 Least prime q such that (r-q)/(q-p), where p are three consecutive primes, produces a new ratio <= 1, arranged by Farey fractions A038566/A038567.

%I A279067 #31 Apr 18 2023 09:44:28
%S A279067 5,11,29,37,6421,367,149,14281,251,701,521,631,84913,127,331,75479,
%T A279067 787,7057,1949,3407,388621,1847,1277,1087,2879,1399,13859,4621,43391,
%U A279067 1657,743507,40213,1151,162209,1973,3491,736577,2579,8039,1264129,14369,43691,4547,4201,8147,29101
%N A279067 Least prime q such that (r-q)/(q-p), where p<q<r are three consecutive primes, produces a new ratio <= 1, arranged by Farey fractions A038566/A038567.
%C A279067 Almost a bisection of A275785 with only the term 5 being in both A279066 & A279067.
%C A279067 The union of A279066 & A279067 is A275785 with only 5 as a common term.
%C A279067 Records: 5, 11, 29, 37, 6421, 14281, 84913, 388621, 743507, 1264129, 1491377, 1613279, 15733451, 27196633, 106132883, 125747441, 304328911, 344278939, 756574061, 1166821769, 2691812749, ..., .
%C A279067 1/n = A179256(n).
%H A279067 Andres Cicuttin and Robert G. Wilson v, <a href="/A279067/b279067.txt">Table of n, a(n) for n = 1..375</a>
%H A279067 Andres Cicuttin and Robert G. Wilson v, <a href="/A279067/a279067.txt">Table of n, Farey fraction = A038566/A038567 and a(n) for n=1..1000, or 0 if no such value is known</a>.
%e A279067 Row 1:        1/1                          5
%e A279067 Row 2:        1/2                         11
%e A279067 Row 3:     1/3  2/3                   29      37
%e A279067 Row 4:     1/4  3/4                 6421     367
%e A279067 Row 5: 1/5 2/5  3/5 4/5       149  14281     251
%e A279067 Row 6:     1/6  5/6                 521      631
%e A279067 Row 7: 1/7    ..    6/7  84913 127  331    75479   787 7057
%e A279067 Row 8: 1/8 3/8  5/8 7/8       1949 3407   388621  1847
%e A279067 etc.
%t A279067 f[n_] := Block[{p = 2, q = 3, r = 5}, While[(r - q) != n(q - p), p = q; q = r; r = NextPrime@ r]; q]; Farey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, 0, b}]; ff = Rest@ Reverse@ Sort[ Farey[25], Denominator[#2] < Denominator[#1] &]; f@# & /@ ff
%Y A279067 Cf. A179234, A275785, A279066.
%K A279067 nonn
%O A279067 1,1
%A A279067 _Andres Cicuttin_ and _Robert G. Wilson v_, Dec 05 2016