A010161 -id:A010161 - cp's OEIS frontend

A010540 Decimal expansion of square root of 89.

9, 4, 3, 3, 9, 8, 1, 1, 3, 2, 0, 5, 6, 6, 0, 3, 8, 1, 1, 3, 2, 0, 6, 6, 0, 3, 7, 7, 6, 2, 2, 6, 4, 0, 7, 1, 6, 9, 8, 3, 6, 2, 2, 6, 3, 3, 4, 1, 5, 1, 2, 1, 3, 2, 0, 6, 6, 2, 9, 8, 1, 4, 4, 8, 9, 8, 0, 0, 2, 2, 9, 0, 9, 5, 8, 5, 1, 1, 8, 0, 5, 8, 5, 4, 1, 0, 2, 6, 9, 8, 6, 8, 9, 0, 3, 8, 4, 1, 0

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {2, 3, 3, 2, 18} repeated. - Harry J. Smith, Jun 10 2009

			9.433981132056603811320660377622640716983622633415121320662981448980022...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2.

Cf. A010161 (continued fraction).

RealDigits[Sqrt[89],10,120][[1]] (* Harvey P. Dale, Nov 20 2011 *)

{ default(realprecision, 20080); x=sqrt(89); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010540.txt", n, " ", d)); } \\ Harry J. Smith, Jun 10 2009

from math import isqrt
def aupton(nn): return list(map(int, str(isqrt(89 * 10**(2*nn)))))[:nn]
print(aupton(100)) # Michael S. Branicky, Sep 04 2021

A041159 Denominators of continued fraction convergents to sqrt(89).

Original entry on oeis.org

1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000, 977001, 2007002, 6998007, 23001023, 53000053, 977001977, 2007004007, 6998013998, 23001046001, 53000106000, 977002954001, 2007006014002, 6998020996007, 23001069002023, 53000159000053, 977003931002977

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1000,0,0,0,0,1).

Cf. A041158, A010161, A020846, A010540.

I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator/@Convergents[Sqrt[89], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0,0,0,0,1000,0,0,0,0,1},{1,2,7,23,53,977,2007,6998,23001,53000},30] (* Harvey P. Dale, Feb 07 2019 *)

G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - Colin Barker, Nov 14 2013

a(n) = 1000*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 12 2013

cp's OEIS Frontend

A010540 Decimal expansion of square root of 89.

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