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.

A272413 Asymptotic mean (normalized by n) of the second longest cycle in a random permutation on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.20958087428418581398902965781534955690113103201623433...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Crossrefs

Cf. A084945, A247398.

Programs

  • Mathematica
    digits = 98; NIntegrate[1 - Exp[ExpIntegralEi[-x]]*(1 - ExpIntegralEi[-x]), {x, 0, 200}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First

Formula

Integral_{0..infinity} 1 - exp(Ei(-x))*(1 - Ei(-x)) dx, where Ei is the exponential integral.

A272414 Asymptotic variance (normalized by n^2) of the second longest cycle in a random permutation on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.012553790635905878147980035846601986785508301199365...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Crossrefs

Cf. A084945, A247398, A272413.

Programs

  • Mathematica
    digits = 98; NIntegrate[x*(1 - E^ExpIntegralEi[-x]*(1 - ExpIntegralEi[-x]) ), {x, 0, 200}, WorkingPrecision -> digits + 5] - NIntegrate[1 - E^ExpIntegralEi[-x]*(1 - ExpIntegralEi[-x]), {x, 0, 200}, WorkingPrecision -> digits + 5]^2 // Join[{0}, RealDigits[#, 10, digits][[1]]]&

Formula

Integral_{0..infinity} x*(1 - exp(Ei(-x))*(1 - Ei(-x))) dx - (integral_{0..infinity} 1 - exp(Ei(-x))*(1 - Ei(-x)) dx)^2, where Ei is the exponential integral.

A272415 Asymptotic mean (normalized by n) of the third longest cycle in a random permutation on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.0883160988831536310105425664298767011723643204511633304667874093...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Crossrefs

Cf. A084945, A247398, A272413, A272414.

Programs

  • Mathematica
    digits = 98; NIntegrate[1 - E^ExpIntegralEi[-x]*(1 - ExpIntegralEi[-x] + (1/2)*ExpIntegralEi[-x]^2), {x, 0, 100}, WorkingPrecision -> digits + 5] // Join[{0}, RealDigits[#, 10, digits][[1]]]&

Formula

Integral_{0..infinity} 1 - e^Ei(-x)*(1 - Ei(-x) + (1/2)*Ei(-x)^2) dx, where Ei is the exponential integral.

A272427 Asymptotic variance (normalized by n^2) of the third longest cycle in a random permutation on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.00449392318179080474794492205756996926493197843077072420750592398...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Crossrefs

Cf. A084945, A247398, A272413, A272414, A272415.

Programs

  • Mathematica
    digits = 98; Ei = ExpIntegralEi; NIntegrate[x*(1 - E^Ei[-x]*(1 - Ei[-x] + (1/2)*Ei[-x]^2)), {x, 0, 100}, WorkingPrecision -> digits + 5] - NIntegrate[1 - E^Ei[-x]*(1 - Ei[-x] + (1/2)*Ei[-x]^2), {x, 0, 100}, WorkingPrecision -> digits + 5]^2 // Join[{0, 0}, RealDigits[#, 10, digits][[1]]]&

Formula

Integral_{0..infinity} x*(1 - e^Ei(-x)*(1 - Ei(-x) + (1/2)*Ei(-x)^2)) dx - (Integral_{0..infinity} 1 - e^Ei(-x)*(1 - Ei(-x) + (1/2)*Ei(-x)^2) dx)^2, where Ei is the exponential integral.
Showing 1-4 of 4 results.

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