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.

5, 11, 29, 37, 6421, 367, 149, 14281, 251, 701, 521, 631, 84913, 127, 331, 75479, 787, 7057, 1949, 3407, 388621, 1847, 1277, 1087, 2879, 1399, 13859, 4621, 43391, 1657, 743507, 40213, 1151, 162209, 1973, 3491, 736577, 2579, 8039, 1264129, 14369, 43691, 4547, 4201, 8147, 29101

Offset

1,1

Comments

Almost a bisection of A275785 with only the term 5 being in both A279066 & A279067.

The union of A279066 & A279067 is A275785 with only 5 as a common term.

Records: 5, 11, 29, 37, 6421, 14281, 84913, 388621, 743507, 1264129, 1491377, 1613279, 15733451, 27196633, 106132883, 125747441, 304328911, 344278939, 756574061, 1166821769, 2691812749, ..., .

1/n = A179256(n).

Links

Andres Cicuttin and Robert G. Wilson v, Table of n, a(n) for n = 1..375

Andres Cicuttin and Robert G. Wilson v, Table of n, Farey fraction = A038566/A038567 and a(n) for n=1..1000, or 0 if no such value is known.

Example

Row 1:        1/1                          5
Row 2:        1/2                         11
Row 3:     1/3  2/3                   29      37
Row 4:     1/4  3/4                 6421     367
Row 5: 1/5 2/5  3/5 4/5       149  14281     251
Row 6:     1/6  5/6                 521      631
Row 7: 1/7    ..    6/7  84913 127  331    75479   787 7057
Row 8: 1/8 3/8  5/8 7/8       1949 3407   388621  1847
etc.

Mathematica

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

Crossrefs

Cf. A179234, A275785, A279066.

Sequence in context: A141561 A240103 A019345 * A049489 A242383 A141785

Adjacent sequences: A279064 A279065 A279066 * A279068 A279069 A279070

Keyword

nonn

Author

Andres Cicuttin and Robert G. Wilson v, Dec 05 2016

Status

approved