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 A040968 Continued fraction for sqrt(1000). 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)