A042936 - OEIS

A042936

Numerators of continued fraction convergents to sqrt(1000).

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

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OFFSET

0,1

LINKS

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).

MATHEMATICA

Numerator[Convergents[Sqrt[1000], 30]] (* Harvey P. Dale, Oct 29 2013 *)

PROG

(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

(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

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

Adjacent sequences: A042933 A042934 A042935 * A042937 A042938 A042939

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved