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A042937
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Denominators of continued fraction convergents to sqrt(1000).
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4
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1, 1, 2, 3, 5, 8, 53, 114, 281, 4329, 8939, 22207, 142181, 164388, 306569, 470957, 777526, 1248483, 78183472, 79431955, 157615427, 237047382, 394662809, 631710191, 4184923955, 9001558101, 22188040157, 341822160456, 705832361069, 1753486882594
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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, 78960998, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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EXAMPLE
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sqrt(1000) = 31.62... = 31 + 1/(1 + 1/(1 + ...)) with convergents 31/1, 32/1, 63/2, 95/3, 158/5, ... - M. F. Hasler, Nov 02 2019
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MATHEMATICA
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Denominator[Convergents[Sqrt[1000], 30]] (* Vincenzo Librandi, Feb 01 2014 *)
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PROG
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(PARI) A42937=contfracpnqn(c=contfrac(sqrt(1000)), #c-1)[2, ] \\ Possibly incorrect last term ignored. NB: a(n) = A42937[n+1]. For more terms use e.g. \p999, or compute any a(n) from this as in A042936. - M. F. Hasler, Nov 01 2019
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CROSSREFS
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Cf. A042936 (numerators), A040968 (continued fraction), A010467 (decimals).
Analog for sqrt(m): A000129 (m=2), A002530 (m=3), A001076 (m=5), A041007 (m=6), A041009 (m=7), A041011 (m=8), A005663 (m=10), A041015 (m=11), A041017 (m=12), ..., A042933 (m=998), A042935 (m=999).
Sequence in context: A041871 A061249 A042237 * A045504 A068500 A272623
Adjacent sequences: A042934 A042935 A042936 * A042938 A042939 A042940
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KEYWORD
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nonn,frac,easy,changed
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Vincenzo Librandi, Feb 01 2014
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STATUS
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approved
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