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.

A078460 Initial n digits in decimal portion of the Traveling Salesman constant (A073008) form a prime number.

Original entry on oeis.org

1, 2, 20, 26, 351, 425, 696
Offset: 1

Views

Author

Jason Earls, Dec 31 2002

Keywords

Comments

a(5), a(6) and a(7) certified prime with Primo.

Examples

			a(2)=2 since 71 is prime.

Crossrefs

Cf. A073008.

A240717 Decimal expansion of 1/sqrt(2*Pi*e), one of the Traveling Salesman constants.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, May 13 2014

Keywords

Comments

This constant is a coefficient in the asymptotics of the minimum tour-length.

Examples

			0.24197072451914334979783019293556...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 497.

Links

Crossrefs

Cf. A000796, A001620, A019633, A073008, A086306, A086307.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); R:= RealField(); 1/Sqrt(2*Pi(R)*Exp(1)); // G. C. Greubel, Aug 19 2018
  • Mathematica
    RealDigits[1/Sqrt[2*Pi*E], 10, 100] // First
  • PARI
    1/sqrt(2*Pi*exp(1)) \\ G. C. Greubel, Aug 19 2018

A242071 Decimal expansion of 'beta', a constant appearing in the random links Traveling Salesman Problem.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Aug 14 2014

Keywords

Examples

			2.041548186412132418045490158381455866340250252564691915512131281...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.5 Traveling Salesman constants, p. 499.

Links

Crossrefs

Cf. A073008, A091505, A240717.

Programs

  • Mathematica
    y[x_] := -2 - ProductLog[-1, E^(-2-x)*(2 - 2*E^x + x)]; beta = (1/2)*NIntegrate[y[x], {x, 0, Infinity}, WorkingPrecision -> 102]; beta // RealDigits // First

Formula

beta = integral_{x>0} y(x) dx, where y(x) = -2 - W_(-1) (e^(-2-x) *(2-2*e^x+x)), W_k(z) being the k-th order Lambert W function (also known as ProductLog). y(x) is implicitly defined by the equation (1+x/2)*exp(-x)+(1+y(x)/2)*exp(-y(x)) = 1.
Showing 1-3 of 3 results.

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

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