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 1-4 of 4 results.

A248287 Egyptian fraction representation of sqrt(62) (A010515) using a greedy function.

Original entry on oeis.org

7, 2, 3, 25, 1483, 4313226, 217223937382030, 165021459996112229693378902726, 190678813907175651157329403848309114198709593621065210721452, 47297173716207795520732599463808376437483496369104651889972118237012796007094238114464594140905135341922378258897840741
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[ 62]]

A010146 Continued fraction for sqrt(62).

Original entry on oeis.org

7, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Eventually periodic with period 4.

Examples

			7.87400787401181101968503444... = 7 + 1/(1 + 1/(6 + 1/(1 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 07 2009

Links

Crossrefs

Cf. A010515 (decimal expansion), A000007.

Programs

  • Magma
    [7] cat &cat[ [1, 6, 1, 14]: n in [1..18]];  // Bruno Berselli, Mar 08 2011
  • Mathematica
    ContinuedFraction[Sqrt[62],300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
Join[{7},LinearRecurrence[{0, 0, 0, 1},{1, 6, 1, 14},72]] (* Ray Chandler, Aug 25 2015 *)
PadRight[{7},120,{14,1,6,1}] (* Harvey P. Dale, Jan 20 2019 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(62)); for (n=0, 20000, write("b010146.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

Formula

a(n) = 1+(1+(-1)^n)*(9+4*i^n)/2 - 7*A000007(n), where i is the imaginary unit. - Bruno Berselli, Mar 08 2011 - Mar 15 2011
From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(2) = 6, a(2^e) = 14 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 5/2^s + 1/2^(2*s-3)). (End)

A041108 Numerators of continued fraction convergents to sqrt(62).

Original entry on oeis.org

7, 8, 55, 63, 937, 1000, 6937, 7937, 118055, 125992, 874007, 999999, 14873993, 15873992, 110117945, 125991937, 1874005063, 1999997000, 13873987063, 15873984063, 236109763945, 251983748008, 1748012251993, 1999996000001, 29747956252007, 31747952252008
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010515, A041109.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[62],30]] (* Harvey P. Dale, Aug 11 2011 *)

Formula

G.f.: -(x^7-7*x^6+8*x^5-55*x^4-63*x^3-55*x^2-8*x-7) / (x^8-126*x^4+1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041109 Denominators of continued fraction convergents to sqrt(62).

Original entry on oeis.org

1, 1, 7, 8, 119, 127, 881, 1008, 14993, 16001, 110999, 127000, 1888999, 2015999, 13984993, 16000992, 237998881, 253999873, 1761998119, 2015997992, 29985970007, 32001967999, 221997778001, 253999746000, 3777994222001, 4031993968001, 27969958030007
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041108, A010146, A020819, A010515.

Programs

  • Magma
    I:=[1, 1, 7, 8, 119, 127, 881, 1008]; [n le 8 select I[n] else 126*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator[Convergents[Sqrt[62], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,126,0,0,0,-1},{1,1,7,8,119,127,881,1008},30] (* Harvey P. Dale, Oct 26 2016 *)

Formula

G.f.: -(x^2-x-1)*(x^4+8*x^2+1) / (x^8-126*x^4+1). - Colin Barker, Nov 12 2013
a(n) = 126*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 12 2013
Showing 1-4 of 4 results.

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

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