A013945 Least d such that period of continued fraction for sqrt(d) contains n (n^2+2 if n odd, (n/2)^2+1 if n even).

3, 2, 11, 5, 27, 10, 51, 17, 83, 26, 123, 37, 171, 50, 227, 65, 291, 82, 363, 101, 443, 122, 531, 145, 627, 170, 731, 197, 843, 226, 963, 257, 1091, 290, 1227, 325, 1371, 362, 1523, 401, 1683, 442, 1851, 485, 2027, 530, 2211, 577, 2403, 626, 2603, 677, 2811

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Examples

			a(3) = 11 because the continued fraction for the square root of 11 is 3, {3, 6}.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Bisections: A164897, A002522.

Programs

Mathematica

Table[If[OddQ[n], n^2 + 2, (n/2)^2 + 1], {n, 100}] (* T. D. Noe, Feb 28 2012 *)

PARI

a(n)=if(n%2, n^2+2, (n/2)^2+1) \\ Charles R Greathouse IV, Aug 09 2017

Formula

G.f.: x(x^5+3x^4-x^3+2x^2+2x+3)/(1-x^2)^3. - N. J. A. Sloane, Jun 12 2004