A040968 Continued fraction for sqrt(1000).

31, 1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1, 1, 62, 1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1, 1, 62, 1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1, 1, 62, 1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1, 1, 62, 1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Comments

After the initial term, periodic with period (1, 1, 1, 1, 1, 6, 2, 2, 15, 2, 2, 6, 1, 1, 1, 1, 1, 62) of length 18. - M. F. Hasler, Nov 02 2019

Links

• C. Elsner, On Error Sums for Square Roots of Positive Integers with Applications to Lucas and Pell Numbers, J. Int. Seq. 17 (2014) # 14.4.4
• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A042936, A042937 (numerators & denominators of convergents).

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(1000)),confrac);

Mathematica

ContinuedFraction[Sqrt[1000],120] (* or *) PadRight[{31},120,{62,1,1,1,1,1,6,2,2,15,2,2,6,1,1,1,1,1}] (* Harvey P. Dale, Aug 22 2018 *)

PARI

A40968=contfrac(sqrt(1000)) \\ For illustration. Better:
A040968(n)={1+if(n%3, abs(n\/18*18-n)>6, n%9, !(n%6)*5, n%18, 14, n, 61, 30)} \\ M. F. Hasler, Nov 02 2019