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

Author

Robert G. Wilson v, Jun 11 2011

Keywords

• easy
• tabf
• nonn

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

Crossrefs

Cf. A133404.

Programs

Mathematica

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