A279066 Least prime q such that (q-p)/(r-q), where p<q<r are three consecutive primes, produces a new ratio <= 1, arranged by Farey fractions A038566/A038567.

5, 3, 31, 23, 8123, 89, 139, 7963, 337, 409, 199, 797, 45439, 113, 953, 88547, 293, 2633, 1933, 3643, 137029, 13381, 523, 2861, 1381, 1259, 7621, 7433, 156157, 3089, 546781, 30911, 1951, 294563, 1129, 3229, 285871, 10369, 14221, 3651341, 25819, 3967, 1669, 6173, 23473, 51383

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.

1/n = A179210(n).

Records: 5, 31, 8123, 45439, 88547, 137029, 156157, 546781, 3651341, 11931613, 16613347, 54636251, 72510257, 102626747, 148379059, 290018137, 847428851, 1165527283, 8232085373, 32592174133, 40113962921, ..., .

Links

Andres Cicuttin and Robert G. Wilson v, Table of n, a(n) for n = 1..322

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                                       3
Row 3:     1/3  2/3                                 31      23
Row 4:     1/4  3/4                               8123      89
Row 5: 1/5 2/5  3/5 4/5                      139  7963     337    409
Row 6:     1/6  5/6                                199     797
Row 7:    1/7 .. 6/7                   45439 113   953   88547    293   2633
Row 8: 1/8 3/8  5/8 7/8                     1933  3643  137029  13381
etc.

Mathematica

f[n_] := Block[{p = 2, q = 3, r = 5}, While[q != n(r - 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. A275785, A279067.

Sequence in context: A290293 A324499 A189747 * A179210 A291843 A187278

Adjacent sequences: A279063 A279064 A279065 * A279067 A279068 A279069

Keyword

nonn,easy

Author

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

Status

approved