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A042936
Numerators of continued fraction convergents to sqrt(1000).
8
31, 32, 63, 95, 158, 253, 1676, 3605, 8886, 136895, 282676, 702247, 4496158, 5198405, 9694563, 14892968, 24587531, 39480499, 2472378469, 2511858968, 4984237437, 7496096405, 12480333842, 19976430247, 132338915324, 284654260895, 701647437114, 10809365817605, 22320379072324
OFFSET
0,1
LINKS
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).
MATHEMATICA
Numerator[Convergents[Sqrt[1000], 30]] (* Harvey P. Dale, Oct 29 2013 *)
PROG
From M. F. Hasler, Nov 01 2019: (Start)
(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])}
\\ But terms with arbitrarily large indices can be computed using:
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)
CROSSREFS
Cf. A042937 (denominators).
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).
Sequence in context: A256496 A133782 A022401 * A042934 A042930 A042932
KEYWORD
nonn,frac,easy
STATUS
approved