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

1,7

Links

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

Formula

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

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 *)

Crossrefs

Cf. A028832, A003285.

Sequence in context: A337542 A282568 A389171 * A024943 A325787 A005929

Adjacent sequences: A028830 A028831 A028832 * A028834 A028835 A028836

Keyword

nonn,nice

Author

Olivier Gérard

Status

approved