A178592 -id:A178592 - cp's OEIS frontend

A178591 Decimal expansion of (9 + sqrt(165))/14.

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

Offset: 1

Klaus Brockhaus, May 30 2010

Continued fraction expansion of (9 + sqrt(165))/14 is A093148.

			(9 + sqrt(165))/14 = 1.56037375561893778715...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A178592 (decimal expansion of sqrt(165)), A093148 (repeat 1, 1, 1, 3).

SetDefaultRealField(RealField(100)); (9+Sqrt(165))/14; // G. C. Greubel, Jan 30 2019

RealDigits[(9+Sqrt[165])/14, 10, 100][[1]] (* G. C. Greubel, Jan 30 2019 *)

default(realprecision, 100); (9+sqrt(165))/14 \\ G. C. Greubel, Jan 30 2019

numerical_approx((9+sqrt(165))/14, digits=100) # G. C. Greubel, Jan 30 2019

A041305 Denominators of continued fraction convergents to sqrt(165).

Original entry on oeis.org

1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272, 4503745, 4685017, 27928830, 60542677, 330642215, 391184892, 9719079623, 10110264515, 60270402198, 130651068911, 713525746753, 844176815664, 20973769322689, 21817946138353

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 (0,0,0,0,0,2158,0,0,0,0,0,-1).

Cf. A041304, A010213, A178592.

I:=[1,1,6,13,71,84,2087,2171,12942,28055,153217, 181272]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Denominator[Convergents[Sqrt[165], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

G.f.: -(x^10 -x^9 +6*x^8 -13*x^7 +71*x^6 -84*x^5 -71*x^4 -13*x^3 -6*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Nov 15 2013

a(n) = 2158*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

More terms from Colin Barker, Nov 15 2013

cp's OEIS Frontend

A178591 Decimal expansion of (9 + sqrt(165))/14.

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