cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A248303 Egyptian fraction representation of sqrt(79) (A010531) using a greedy function.

Original entry on oeis.org

8, 2, 3, 19, 449, 428533, 9269693581837, 91606099704009514713682461, 9363306451087445468962351366467752586530744299460793, 108004048445456272073056808573911074497485924169946430496208965479597773835656564948730792745155753648476
Offset: 0

Views

Author

Robert G. Wilson v, Oct 04 2014

Keywords

Crossrefs

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.
Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Programs

  • Mathematica
    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[ 79]]

A010157 Continued fraction for sqrt(79).

Original entry on oeis.org

8, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			8.88819441731558885009144167... = 8 + 1/(1 + 1/(7 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 09 2009

Links

Crossrefs

Cf. A010531 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[79],300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 23000); x=contfrac(sqrt(79)); for (n=0, 20000, write("b010157.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

Formula

From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(2) = 7, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 3/2^(s-1) + 9/4^s). (End)

A041140 Numerators of continued fraction convergents to sqrt(79).

Original entry on oeis.org

8, 9, 71, 80, 1351, 1431, 11368, 12799, 216152, 228951, 1818809, 2047760, 34582969, 36630729, 290998072, 327628801, 5533058888, 5860687689, 46557872711, 52418560400, 885254839111, 937673399511, 7448968635688, 8386642035199, 141635241198872, 150021883234071
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010531, A041141.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[79], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,0,0,160,0,0,0,-1},{8,9,71,80,1351,1431,11368,12799},30] (* Harvey P. Dale, Sep 08 2024 *)

Formula

G.f.: -(x^7-8*x^6+9*x^5-71*x^4-80*x^3-71*x^2-9*x-8) / (x^8-160*x^4+1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041141 Denominators of continued fraction convergents to sqrt(79).

Original entry on oeis.org

1, 1, 8, 9, 152, 161, 1279, 1440, 24319, 25759, 204632, 230391, 3890888, 4121279, 32739841, 36861120, 622517761, 659378881, 5238169928, 5897548809, 99598950872, 105496499681, 838074448639, 943570948320, 15935209621759, 16878780570079
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041140, A010157, A020836, A010531.

Programs

  • Magma
    I:=[1,1,8,9,152,161,1279,1440]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator/@Convergents[Sqrt[79], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 9 x^2 + 1)/(x^8 - 160 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,160,0,0,0,-1},{1,1,8,9,152,161,1279,1440},40] (* Harvey P. Dale, Aug 09 2021 *)

Formula

G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-160*x^4+1). - Colin Barker, Nov 13 2013
a(n) = 160*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

A177035 Decimal expansion of sqrt(13493990).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 01 2010

Keywords

Comments

Continued fraction expansion of sqrt(13493990) is 3673 followed by (repeat 2, 2, 2, 7346).
sqrt(13493990) = sqrt(2)*sqrt(5)*sqrt(19)*sqrt(29)*sqrt(31)*sqrt(79).

Examples

			sqrt(13493990) = 3673.41666572143705136693...

Crossrefs

Cf. A002193 (decimal expansion of sqrt(2)), A002163 (decimal expansion of sqrt(5)), A010475 (decimal expansion of sqrt(19)), A010484 (decimal expansion of sqrt(29)), A010486 (decimal expansion of sqrt(31)), A010531 (decimal expansion of sqrt(79)), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165).

Programs

  • Mathematica
    RealDigits[Sqrt[13493990],10,120][[1]] (* Harvey P. Dale, Nov 11 2016 *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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