A020640 Increasing periods of continued fraction for sqrt(n) (period of continued fraction for sqrt(A013645(n))).

1, 2, 4, 5, 6, 8, 10, 12, 16, 18, 20, 22, 26, 34, 37, 40, 42, 44, 48, 52, 54, 60, 62, 64, 70, 76, 79, 88, 94, 96, 102, 104, 108, 114, 118, 122, 130, 136, 152, 156, 158, 170, 172, 174, 194, 196, 202, 207, 210, 217, 228, 234, 238, 239, 248, 262, 268, 280, 281

Offset

1,2

Links

Patrick McKinley, Table of n, a(n) for n=1..512

Mathematica

per[n_] := ContinuedFraction[Sqrt[n]][[2]] // Length; record = 0; t = Reap[For[n = 1, n < 2*10^4, n++, If[ !IntegerQ[Sqrt[n]], p = per[n]; If[p > record, record = p; Print[{n, p}]; Sow[{n, p}]]]]][[2, 1]]; A020640 = t[[All, 2]] (* Jean-François Alcover, Dec 27 2012 *)
DeleteDuplicates[Table[If[IntegerQ[Sqrt[n]], Nothing, Length[ContinuedFraction[Sqrt[n]][[2]]]], {n, 20000}], GreaterEqual] (* Harvey P. Dale, Dec 28 2023 *)

Crossrefs

Sequence in context: A371447 A091413 A371448 * A068383 A276603 A175416

Adjacent sequences: A020637 A020638 A020639 * A020641 A020642 A020643

Keyword

nonn,nice

Author

David W. Wilson

Status

approved