%I #28 Mar 25 2026 23:58:22

%S 31,32,63,95,158,253,1676,3605,8886,136895,282676,702247,4496158,

%T 5198405,9694563,14892968,24587531,39480499,2472378469,2511858968,

%U 4984237437,7496096405,12480333842,19976430247,132338915324,284654260895,701647437114,10809365817605,22320379072324

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

%H Vincenzo Librandi, <a href="/A042936/b042936.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).

%t Numerator[Convergents[Sqrt[1000], 30]] (* _Harvey P. Dale_, Oct 29 2013 *)

%o (PARI) A42936=contfracpnqn(c=contfrac(sqrt(1000)), #c)[1,][^-1] \\ Discards possibly incorrect last term. NB: a(n)=A42936[n+1]. Could be extended using: {A42936=concat(A42936, 78960998*A42936[-18..-1]-A42936[-36..-19])} \\ _M. F. Hasler_, Nov 01 2019

%o (PARI) A042936(n)={[A42936[n%18+i]|i<-[1, 19]]*([0, -1; 1, 78960998]^(n\18))[,1]} \\ Faster but longer with n=divrem(n,18), _M. F. Hasler_, Nov 01 2019

%Y Cf. A042937 (denominators).

%Y Analog for sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042934 (m=999).

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_