A010545 -id:A010545 - cp's OEIS frontend

A248317 Egyptian fraction representation of sqrt(94) (A010545) using a greedy function.

9, 2, 6, 35, 8223, 105523068, 11519554345709228, 1494630770210131639238952310389890, 3373102223355000280957265659458842393059982648952025309066380048000, 11877410529374051888559091719126415241014959874914182236570178526215397825159914010265110751425103744082344062654761136352199992571445

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[ 94]]

A010165 Continued fraction for sqrt(94).

Original entry on oeis.org

9, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1

Offset: 0

N. J. A. Sloane

			9.695359714832658028148881150... = 9 + 1/(1 + 1/(2 + 1/(3 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 11 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A010545 Decimal expansion. - Harry J. Smith, Jun 11 2009

ContinuedFraction[Sqrt[94],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9},120,{18,1,2,3,1,1,5,1,8,1,5,1,1,3,2,1}] (* Harvey P. Dale, Aug 20 2020 *)

{ allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(94)); for (n=0, 20000, write("b010165.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

A041168 Numerators of continued fraction convergents to sqrt(94).

Original entry on oeis.org

9, 10, 29, 97, 126, 223, 1241, 1464, 12953, 14417, 85038, 99455, 184493, 652934, 1490361, 2143295, 40069671, 42212966, 124495603, 415699775, 540195378, 955895153, 5319671143, 6275566296, 55524201511

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, 0, 0, 0, 0, 0, 0, 0, 0, 4286590, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Cf. A010545, A041169.

Numerator[Convergents[Sqrt[94], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

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A248317 Egyptian fraction representation of sqrt(94) (A010545) using a greedy function.

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A010165 Continued fraction for sqrt(94).

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A041168 Numerators of continued fraction convergents to sqrt(94).

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