A191607 - OEIS

%I #21 Mar 28 2015 22:38:11

%S 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,

%T 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,

%U 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

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

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

%C 1, 0

%C 1, 1, 0

%C 1, 2, 1, 1, 0

%C 1, 3, 2, 1, 1, 1, 0

%C 1, 4, 3, 2, 3, 1, 2, 1, 1, 1, 0

%C etc.

%C Row n has A005728(n) terms. - _Michel Marcus_, Jun 27 2014

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

%Y Cf. A133404.

%K easy,tabf,nonn

%O 1,7

%A _Robert G. Wilson v_, Jun 11 2011