A010151 -id:A010151 - cp's OEIS frontend

A010525 Decimal expansion of square root of 73.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 8 followed by {1, 1, 5, 5, 1, 1, 16} repeated. - Harry J. Smith, Jun 08 2009

			8.544003745317531167871648326239706434594455329533282241908651253771648....

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

Cf. A010151 (continued fraction).

RealDigits[N[73^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 23 2012 *)

default(realprecision, 20080); x=sqrt(73); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010525.txt", n, " ", d));  \\ Harry J. Smith, Jun 08 2009

Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009

A041129 Denominators of continued fraction convergents to sqrt(73).

Original entry on oeis.org

1, 1, 2, 11, 57, 68, 125, 2068, 2193, 4261, 23498, 121751, 145249, 267000, 4417249, 4684249, 9101498, 50191739, 260060193, 310251932, 570312125, 9435245932, 10005558057, 19440803989, 107209578002, 555488693999, 662698272001, 1218186966000, 20153689728001

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 (0,0,0,0,0,0,2136,0,0,0,0,0,0,1).

Cf. A041128, A010151, A020830, A010525.

I:=[1,1,2,11,57,68,125,2068,2193,4261,23498,121751,145249, 267000]; [n le 14 select I[n] else 2136*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Denominator/@Convergents[Sqrt[73], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^12 - x^11 + 2 x^10 - 11 x^9 + 57 x^8 - 68 x^7 + 125 x^6 + 68 x^5 + 57 x^4 + 11 x^3 + 2 x^2 + x + 1)/(x^14 + 2136 x^7 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

G.f.: -(x^12 -x^11 +2*x^10 -11*x^9 +57*x^8 -68*x^7 +125*x^6 +68*x^5 +57*x^4 +11*x^3 +2*x^2 +x +1) / (x^14 +2136*x^7 -1). - Colin Barker, Nov 13 2013

a(n) = 2136*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 11 2013

cp's OEIS Frontend

A010525 Decimal expansion of square root of 73.

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