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Denominators of continued fraction convergents to sqrt(1000).
4

%I #23 Jun 26 2022 23:37:00

%S 1,1,2,3,5,8,53,114,281,4329,8939,22207,142181,164388,306569,470957,

%T 777526,1248483,78183472,79431955,157615427,237047382,394662809,

%U 631710191,4184923955,9001558101,22188040157,341822160456,705832361069,1753486882594

%N Denominators of continued fraction convergents to sqrt(1000).

%H Vincenzo Librandi, <a href="/A042937/b042937.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, 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).

%e 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

%t Denominator[Convergents[Sqrt[1000], 30]] (* _Vincenzo Librandi_, Feb 01 2014 *)

%o (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

%Y Cf. A042936 (numerators), A040968 (continued fraction), A010467 (decimals).

%Y 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).

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Feb 01 2014