A010163 -id:A010163 - cp's OEIS frontend

A010543 Decimal expansion of square root of 92.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {1, 1, 2, 4, 2, 1, 1, 18} repeated. - Harry J. Smith, Jun 11 2009

			9.5916630466254390831948761283253878399934...

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

Cf. A010163 (continued fraction).

Cf. A010479.

RealDigits[N[Sqrt[92],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 04 2012 *)

{ default(realprecision, 20080); x=sqrt(92); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010543.txt", n, " ", d)); } \\ Harry J. Smith, Jun 11 2009

from math import isqrt
def aupton(nn): return list(map(int, str(isqrt(92 * 10**(2*nn)))))[:nn]
print(aupton(100)) # Michael S. Branicky, Sep 05 2021

Equals 2 * A010479.

A041165 Denominators of continued fraction convergents to sqrt(92).

Original entry on oeis.org

1, 1, 2, 5, 22, 49, 71, 120, 2231, 2351, 4582, 11515, 50642, 112799, 163441, 276240, 5135761, 5412001, 10547762, 26507525, 116577862, 259663249, 376241111, 635904360, 11822519591, 12458423951, 24280943542, 61020311035, 268362187682, 597744686399

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 (0,0,0,0,0,0,0,2302,0,0,0,0,0,0,0,-1).

Cf. A041164, A010163, A020849, A010543.

I:=[1, 1, 2, 5, 22, 49, 71, 120, 2231, 2351, 4582, 11515, 50642, 112799, 163441, 276240]; [n le 16 select I[n] else 2302*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator[Convergents[Sqrt[92], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

G.f.: -(x^14 -x^13 +2*x^12 -5*x^11 +22*x^10 -49*x^9 +71*x^8 -120*x^7 -71*x^6 -49*x^5 -22*x^4 -5*x^3 -2*x^2 -x -1) / ((x^8 -48*x^4 +1)*(x^8 +48*x^4 +1)). - Colin Barker, Nov 14 2013

a(n) = 2302*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

More terms from Colin Barker, Nov 14 2013

cp's OEIS Frontend

A010543 Decimal expansion of square root of 92.

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