A010162 -id:A010162 - cp's OEIS frontend

A010542 Decimal expansion of square root of 91.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {1, 1, 5, 1, 5, 1, 1, 18} repeated. - Harry J. Smith, Jun 11 2009

			9.53939201416945649152621586023226540254623...

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

Cf. A010162 (continued fraction).

RealDigits[N[Sqrt[91],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 04 2012 *)

{ default(realprecision, 20080); x=sqrt(91); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010542.txt", n, " ", d)); } \\ Harry J. Smith, Jun 11 2009

from math import isqrt
def aupton(nn): return list(map(int, str(isqrt(91 * 10**(2*nn)))))[:nn]
print(aupton(100)) # Michael S. Branicky, Sep 05 2021

A041163 Denominators of continued fraction convergents to sqrt(91).

Original entry on oeis.org

1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420, 9629731, 10149151, 19778882, 109043561, 128822443, 753155776, 881978219, 1635133995, 30314390129, 31949524124, 62263914253, 343269095389, 405533009642, 2370934143599

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 (0,0,0,0,0,0,0,3148,0,0,0,0,0,0,0,-1).

Cf. A041162, A010162, A020848, A010542.

I:=[1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420]; [n le 16 select I[n] else 3148*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator[Convergents[Sqrt[91], 30]] (* Bruno Berselli, Nov 14 2013 *)
CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 11 x^11 + 13 x^10 - 76 x^9 + 89 x^8 - 165 x^7 - 89 x^6 - 76 x^5 - 13 x^4 - 11 x^3 - 2 x^2 - x - 1)/(x^16 - 3148 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

G.f.: -(x^14 -x^13 +2*x^12 -11*x^11 +13*x^10 -76*x^9 +89*x^8 -165*x^7 -89*x^6 -76*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / (x^16 -3148*x^8 +1). - Colin Barker, Nov 14 2013

a(n) = 3148*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

More terms from Colin Barker, Nov 14 2013

cp's OEIS Frontend

A010542 Decimal expansion of square root of 91.

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