A191607 Table of the difference of numerator and denominator of Farey sequences, read by rows.

1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 3, 2, 1, 1, 1, 0, 1, 4, 3, 2, 3, 1, 2, 1, 1, 1, 0, 1, 5, 4, 3, 2, 3, 1, 2, 1, 1, 1, 1, 0, 1, 6, 5, 4, 3, 5, 2, 3, 4, 1, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 7, 6, 5, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 1, 1, 0, 1, 8, 7, 6, 5, 4, 7, 3, 5, 2, 5, 3, 4, 5, 1, 4, 3, 2, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1, 0

Offset

1,7

Comments

For n>=1, the n-th row begins with 1, n-1 and ends with 1, 0.

1, 0

1, 1, 0

1, 2, 1, 1, 0

1, 3, 2, 1, 1, 1, 0

1, 4, 3, 2, 3, 1, 2, 1, 1, 1, 0

etc.

Row n has A005728(n) terms. - Michel Marcus, Jun 27 2014

Links

Table of n, a(n) for n=1..112.

Mathematica

Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[ -Numerator@ Farey@ n + Denominator@ Farey@ n, {n, 9}] // Flatten

Crossrefs

Cf. A133404.

Sequence in context: A174295 A158511 A092921 * A029387 A070878 A228128

Adjacent sequences: A191604 A191605 A191606 * A191608 A191609 A191610

Keyword

easy,tabf,nonn

Author

Robert G. Wilson v, Jun 11 2011

Status

approved