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.

Previous Showing 21-25 of 25 results.

A272429 Asymptotic mean (normalized by n) of the second largest connected component in a random mapping on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.17090961985966239214460728413311738704719072962628832355853881...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random mapping statistics, p. 290.

Links

Crossrefs

Cf. A084945, A143297, A261873.

Programs

  • Mathematica
    digits = 95; Ei = ExpIntegralEi; 2*NIntegrate[1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2), {x, 0, 200}, WorkingPrecision -> digits + 5] // RealDigits[#, 10, digits]& // First

Formula

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

A380270 Decimal expansion of Integral_{x=1..A070769} li(x) dx (negated), where li(x) is the logarithmic integral.

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jan 18 2025

Keywords

Comments

A070769 is Soldner's constant, where li(A070769)=0.
Integral_{x=0..1} li(x) dx = -log(2) then Integral_{x=0..A070769} li(x) dx = A380270 - log(2) = -1.19324951683011591582919049...

Examples

			-0.500102336270170606411958373..

Crossrefs

Cf. A069284, A070769, A084945, A091723, A244067, A257817, A257818, A257819, A257820, A257821, A270857.

Programs

  • Mathematica
    y = x /. FindRoot[LogIntegral[x] == 0, {x, 1.5}, WorkingPrecision -> 200]; yy = -Integrate[LogIntegral[x], {x, 1, y}]; RealDigits[yy, 10, 105][[1]]

A225242 First occurrence of n consecutive n's in the decimal expansion of the Golomb-Dickman constant.

Original entry on oeis.org

28, 256, 1967, 387
Offset: 1

Views

Author

Eric W. Weisstein, Jul 25 2013

Keywords

Comments

Earls sequence of the Golomb-Dickman constant.
a(5) > 15000.

Examples

			lambda = 0.62432998854355087099293638310...1822161..., so
a(1) = 28 (one 1 first appears at digit 28),
a(2) = 256 (two 2s first occur starting at digit 256).

Links

Crossrefs

Cf. A084945 (decimal expansion of the Golomb-Dickman constant).

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.

A272430 Asymptotic variance (normalized by n^2) of the second largest connected component in a random mapping on n symbols.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 29 2016

Keywords

Examples

			0.01862022330678138872140657036234315043193560144957499823184259199928...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random mapping statistics, p. 290.

Links

Crossrefs

Cf. A084945, A143297, A261873, A272429.

Programs

  • Mathematica
    digits = 98; Ei = ExpIntegralEi; (8/3)*NIntegrate[x*(1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2)), {x, 0, 200}, WorkingPrecision -> digits + 5] - 4*NIntegrate[1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2), {x, 0, 200}, WorkingPrecision -> digits + 5]^2 // Join[{0}, RealDigits[#, 10, digits][[1]]]&

Formula

(8/3)*integral_{0..infinity} x*(1 - e^(Ei(-x)/2)*(1 - Ei(-x)/2)) dx - 4*(integral_{0..infinity} 1 - e^(Ei(-x)/2)*(1 - Ei(-x)/2) dx)^2, where Ei is the exponential integral.
Previous Showing 21-25 of 25 results.

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