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

0,1

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

Table of n, a(n) for n=0..88.

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).

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A221432 A085012 A086019 * A040967 A040965 A040966

Adjacent sequences: A040965 A040966 A040967 * A040969 A040970 A040971

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane.

Status

approved