A042934 Numerators of continued fraction convergents to sqrt(999).

31, 32, 63, 95, 158, 885, 5468, 6353, 37233, 80819, 441328, 522147, 3574210, 18393197, 21967407, 40360604, 62328011, 102688615, 6429022141, 6531710756, 12960732897, 19492443653, 32453176550

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, 205377230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

a(n) = 205377230*a(n-18) - a(n-36). - Wesley Ivan Hurt, May 28 2021

Mathematica

Numerator[Convergents[Sqrt[999], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

Prog

(PARI) A42934=contfracpnqn(c=contfrac(sqrt(999)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n) = A42934[n+1]! For more terms, use:
A042934(n)={n<#A42934 || A42934_upto(n+10); A42934[n+1]}
{A42934_upto(N, A=Vec(A42934, N))=for(n=#A42934+1, N, A[n]=205377230*A[n-18]-A[n-36]); A42934=A} \\ M. F. Hasler, Nov 01 2019

Crossrefs

Cf. A042935 (denominators).

Analog for other 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), ..., A042936 (m=1000).

Sequence in context: A133782 A022401 A042936 * A042930 A042932 A042928

Adjacent sequences: A042931 A042932 A042933 * A042935 A042936 A042937

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Status

approved