A028833 Index of redundancy in period of continued fraction for sqrt(n).

0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 2, 0, 3, 2, 1, 0, 0, 0, 0, 1, 2, 0, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 6, 5, 3, 7, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 3, 5, 2, 1, 6, 1, 0, 0, 0, 0, 5, 0, 4, 3, 4, 0, 4, 3, 2, 7, 2, 1, 1, 0, 0, 0, 0, 0, 2, 6, 0, 3, 2, 0, 5, 4, 6, 10, 1, 1, 8, 1, 0, 0, 0, 0

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• nice

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A028832, A003285.

Programs

Mathematica

a[n_] := If[IntegerQ[Sqrt[n]], 0, Length[p = ContinuedFraction[Sqrt[n]] // Last] - Length[p // Union]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Dec 26 2012 *)

Formula

a(n) = A003285(n) - A028832(n).