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 1-3 of 3 results.

A093064 Decimal expansion of (4 + 3*log(3))/20.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Mar 16 2004

Keywords

Comments

Average length of a line picked at random inside an equilateral triangle with unit side lengths.

Examples

			0.364791843...

Links

Crossrefs

Cf. A093063.

Programs

A180307 Decimal expansion of the mean length of a line segment picked at random in a 3, 4, 5 (right) triangle.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Aug 25 2010

Keywords

Examples

			1.4581846347360227433...

Links

Crossrefs

Cf. A093063.

Programs

  • Magma
    SetDefaultRealField(RealField(111)); (20460 +9728*Log(2) +5103*Log(3) )/22500; // G. C. Greubel, Dec 20 2019
  • Maple
    evalf( (20460+9728*log(2)+5103*log(3))/22500, 111); # G. C. Greubel, Dec 20 2019
  • Mathematica
    F[a_, b_, c_]:= (a^3 +b^3 +2*c^3)/(15*c^2) +(a^2/(15*b))*(1 + (b/c)^3)* ArcCsch[a/b] +(b^2/(15*a))*(1 +(a/c)^3)*ArcCsch[b/a]; RealDigits[F[3, 4, 5], 10, 110][[1]] (* G. C. Greubel, Dec 20 2019 *)
  • PARI
    arcsch(z)=log(1/z+sqrt(1/z^2+1));
seglen(a,b)={my(c=sqrt(a^2+b^2));(a^3+b^3+2*c^3)/(15*c^2)+(a^2/(15*b))*(1+(b/c)^3)*arcsch(a/b)+(b^2/(15*a))*(1+(a/c)^3)*arcsch(b/a)};
seglen(3,4) \\ Hugo Pfoertner, Dec 18 2019
  • Sage
    def F(a, b, c): return (a^3 + b^3 + 2*c^3)/(15*c^2) + (a^2/(15*b))*(1 + (b/c)^3)*arccsch(a/b) + (b^2/(15*a))*(1 + (a/c)^3)*arccsch(b/a)
numerical_approx(F(3,4,5), digits=110) # G. C. Greubel, Dec 20 2019

Formula

Equals (20460 + 9728*log(2) + 5103*log(3))/22500.
Equals (a^3 + b^3 + 2*c^3) / (15*c^2) + (a^2 / (15*b)) * (1 + (b/c)^3) * cosech^{-1}(a/b) + (b^2 / (15*a)) * (1 + (a/c)^3) * cosech^{-1}(b/a) for an arbitrary right angled triangle with sides a, b and (hypotenuse) c. - Muthu Veerappan Ramalingam, Dec 18 2019

A180308 Decimal expansion of the mean length of a line segment picked at random in a 30-60-90 (right) triangle.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Aug 25 2010

Keywords

Examples

			0.28857171834839485625...

Links

Crossrefs

Cf. A093063, A093064, A180307.

Programs

  • Mathematica
    RealDigits[(204 + 36*Sqrt[3] + 81*Log[3] + 2*(9 + 8*Sqrt[3])*Log[2 + Sqrt[3]])/1440, 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

Formula

Equals (204 + 36*sqrt(3) + 81*log(3) + 2*(9 + 8*sqrt(3))*log(2 + sqrt(3)))/1440.
Showing 1-3 of 3 results.

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