A010539 -id:A010539 - cp's OEIS frontend

A248311 Egyptian fraction representation of sqrt(88) (A010539) using a greedy function.

9, 3, 22, 490, 354041, 1208217960776, 4186940633541789679127193, 76474669481022771277404940186836961906372402204599, 7594258642248803079765161740266796480079825999844206739159205729216343587849398469094469783005401105

Offset: 0

Robert G. Wilson v, Oct 04 2014

nonn

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.

Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 88]]

A378206 Decimal expansion of the inradius of a triakis tetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Nov 21 2024

The triakis tetrahedron is the dual polyhedron of the truncated tetrahedron.

			0.53300179088902608574609433108459844097593504016042...

Index entries for algebraic numbers, degree 2.

Cf. A378204 (surface area), A378205 (volume), A378207 (midradius), A378208 (dihedral angle).

Cf. A010539.

First[RealDigits[5/Sqrt[88], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisTetrahedron", "Inradius"], 10, 100]]

Equals 5/(2*sqrt(22)) = 5/A010539.

A010160 Continued fraction for sqrt(88).

Original entry on oeis.org

9, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1

Offset: 0

N. J. A. Sloane

			9.380831519646859109131260227... = 9 + 1/(2 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 10 2009

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).

Cf. A010539 Decimal expansion. - Harry J. Smith, Jun 10 2009

ContinuedFraction[Sqrt[88],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)

{ allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(88)); for (n=0, 20000, write("b010160.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

A041156 Numerators of continued fraction convergents to sqrt(88).

Original entry on oeis.org

9, 19, 28, 47, 75, 197, 3621, 7439, 11060, 18499, 29559, 77617, 1426665, 2930947, 4357612, 7288559, 11646171, 30580901, 562102389, 1154785679, 1716888068, 2871673747, 4588561815, 12048797377, 221466914601

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 (0,0,0,0,0,394,0,0,0,0,0,-1).

Cf. A010539, A041157.

Numerator[Convergents[Sqrt[88], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^11-9*x^10+19*x^9-28*x^8+47*x^7-75*x^6-197*x^5-75*x^4-47*x^3-28*x^2-19*x-9)/(x^12-394*x^6+1). [Colin Barker, Jul 18 2012]

A041157 Denominators of continued fraction convergents to sqrt(88).

Original entry on oeis.org

1, 2, 3, 5, 8, 21, 386, 793, 1179, 1972, 3151, 8274, 152083, 312440, 464523, 776963, 1241486, 3259935, 59920316, 123100567, 183020883, 306121450, 489142333, 1284406116, 23608452421, 48501310958, 72109763379, 120611074337, 192720837716, 506052749769

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 (0,0,0,0,0,394,0,0,0,0,0,-1).

Cf. A010539, A041156.

Denominator/@Convergents[Sqrt[88], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 5 x^7 + 8 x^6 - 21 x^5 - 8 x^4 - 5 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)
LinearRecurrence[{0,0,0,0,0,394,0,0,0,0,0,-1},{1,2,3,5,8,21,386,793,1179,1972,3151,8274},30] (* Harvey P. Dale, Jul 28 2017 *)

a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-5*x^7+8*x^6 -21*x^5 -8*x^4 -5*x^3-3*x^2-2*x-1) / (x^12-394*x^6+1). - Colin Barker, Jul 18 2012

cp's OEIS Frontend

A248311 Egyptian fraction representation of sqrt(88) (A010539) using a greedy function.

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A378206 Decimal expansion of the inradius of a triakis tetrahedron with unit shorter edge length.

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A010160 Continued fraction for sqrt(88).

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PARI

A041156 Numerators of continued fraction convergents to sqrt(88).

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A041157 Denominators of continued fraction convergents to sqrt(88).

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