cp's OEIS Frontend

A042936 Numerators of continued fraction convergents to sqrt(1000).

%I A042936 #26 Jun 26 2022 23:36:50
%S A042936 31,32,63,95,158,253,1676,3605,8886,136895,282676,702247,4496158,
%T A042936 5198405,9694563,14892968,24587531,39480499,2472378469,2511858968,
%U A042936 4984237437,7496096405,12480333842,19976430247,132338915324,284654260895,701647437114,10809365817605,22320379072324
%N A042936 Numerators of continued fraction convergents to sqrt(1000).
%H A042936 Vincenzo Librandi, <a href="/A042936/b042936.txt">Table of n, a(n) for n = 0..200</a>
%H A042936 <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 A042936 Numerator[Convergents[Sqrt[1000], 30]] (* _Harvey P. Dale_, Oct 29 2013 *)
%o A042936 From  _M. F. Hasler_, Nov 01 2019: (Start)
%o A042936 (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])}
%o A042936 \\ But terms with arbitrarily large indices can be computed using:
%o A042936 A042936(n)={[A42936[n%18+i]|i<-[1, 19]]*([0, -1; 1, 78960998]^(n\18))[,1]} \\ Faster but longer with n=divrem(n,18). (End)
%Y A042936 Cf. A042937 (denominators).
%Y A042936 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 A042936 nonn,frac,easy
%O A042936 0,1
%A A042936 _N. J. A. Sloane_