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 1-2 of 2 results.

A178567 Decimal expansion of sqrt(1297).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 29 2010

Keywords

Comments

Continued fraction expansion of sqrt(1297) is 36 followed by (repeat 72).
1297 is prime.

Examples

			sqrt(1297) = 36.01388621073821297137...

Links

Crossrefs

Cf. A178566 (decimal expansion of (32+sqrt(1297))/13).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Sqrt(1297); // G. C. Greubel, Jan 30 2019
  • Mathematica
    RealDigits[Sqrt[1297],10,120][[1]] (* Harvey P. Dale, Oct 10 2011 *)
  • PARI
    default(realprecision, 100); sqrt(1297) \\ G. C. Greubel, Jan 30 2019
  • Sage
    numerical_approx(sqrt(1297), digits=100) # G. C. Greubel, Jan 30 2019

A164360 Period 3: repeat [5, 4, 3].

Original entry on oeis.org

5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3
Offset: 0

Views

Author

Stephen Crowley, Aug 14 2009

Keywords

Comments

From Klaus Brockhaus, May 29 2010: (Start)
Continued fraction expansion of (32+sqrt(1297))/13.
Decimal expansion of 181/333. (End)

Links

Crossrefs

Cf. A007877 (repeat 0,1,2,1), A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2), A158289 (repeat 0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1).
Cf. A178566 (decimal expansion of (32+sqrt(1297))/13). [Klaus Brockhaus, May 29 2010]

Programs

Formula

a(n) = 4+(-1)^n*((1/2+I*sqrt(3)/6)*((1+I*sqrt(3))/2)^n+(1/2-I*sqrt(3)/6)*((1-I*sqrt(3))/2)^n). [Corrected by Klaus Brockhaus, Sep 17 2009]
a(n) = 4+(1/3)*sqrt(3)*sin(2*n*Pi/3)+cos(2*n*Pi/3). [Corrected by Klaus Brockhaus, Sep 17 2009]
a(n) = a(n-3) for n > 2, with a(0) = 5, a(1) = 4, a(2) = 3.
G.f.: (5+4*x+3*x^2)/((1-x)*(1+x+x^2)). [Klaus Brockhaus, Sep 17 2009]
E.g.f.: 4*exp(x)+(1/3)*sqrt(3)*exp(-(1/2)*x)*sin((1/2)*x*sqrt(3))+exp(-(1/2)*x)*cos((1/2)*x*sqrt(3)).
a(n) = 4 + A057078(n). - Wesley Ivan Hurt, Jul 01 2016

Extensions

Edited by Klaus Brockhaus, Sep 17 2009
Offset changed to 0 and formulas adjusted by Klaus Brockhaus, May 18 2010
Showing 1-2 of 2 results.

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