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.

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A134883 Decimal expansion of Sum_{n>=1} 1/(n^n+1).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Nov 15 2007

Keywords

Comments

Constant formed from sum of reversed Sierpinski numbers of first kind A014566.

Examples

			0.7399479434954655122560255307349947820561106657422439628745456519998...

Crossrefs

Cf. A014566, A073009, A100085, A134877, A134878, A134879, A134880, A134881, A134882.

Programs

  • Mathematica
    RealDigits[N[Sum[1/(n^n + 1), {n, 1, 150}], 100]][[1]] (* first zero removed *)

A135608 Decimal expansion of Sum_{n>=2} 1/n^(n+1).

Original entry on oeis.org

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

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Feb 27 2008

Keywords

Links

Crossrefs

Cf. A073009.

Programs

  • Maple
    P:=proc(n) local a,i; a:=0; for i from 1 by 1 to n do a:=a+i^(-i-1); print(evalf(a-1,101)); od; end: P(100);
  • Mathematica
    digits = 100; NSum[1/(n^(n+1)), {n, 2, Infinity}, NSumTerms -> 100, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
  • PARI
    suminf(n=2, 1/n^(n+1)) \\ Michel Marcus, Oct 23 2016

Extensions

Lower summation index in definition corrected by R. J. Mathar, Jan 26 2009

A229191 Decimal expansion of the integral_{x=0..Infinity} 1/x^x dx.

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Sep 15 2013

Keywords

Comments

"The function x^x grows even more quickly than Gamma(x) and the integral {0-inf} 1/x^x dx = 1.9954559575... and the integral {1-inf} 1/x^x dx = 0.7041699604... ." [Finch]

Examples

			1.9954559575001380004187246984527243520862166369679788727883...

References

  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 263.

Crossrefs

Cf. A058655, A073009, A245637.

Programs

  • Maple
    evalf(int(1/x^x, x=0..infinity), 120);  # Alois P. Heinz, Dec 30 2021
  • Mathematica
    RealDigits[ NIntegrate[ 1/x^x, {x, 0, 100}, MaxRecursion -> 5000, MaxPoints -> 5000, AccuracyGoal-> 111, PrecisionGoal -> 111, WorkingPrecision -> 120], 10, 111][[1]]

A077178 Continued fraction expansion of Sum_{k >= 1} 1/k^k.

Original entry on oeis.org

1, 3, 2, 3, 4, 3, 1, 2, 1, 1, 6, 7, 2, 5, 3, 1, 2, 1, 8, 1, 2, 4, 1, 9, 3, 1, 1, 18, 1, 1, 29, 4, 1, 5, 2, 167, 1, 62, 4, 2, 1, 3, 3, 27, 1, 9, 1, 46, 1, 3, 2, 2, 1, 1, 3, 2, 10, 73, 1, 11, 1, 2, 1, 1, 18, 1, 4, 1, 4, 6, 1, 4, 4, 1, 6, 1, 1, 1, 2, 1, 7, 8, 4, 1, 3, 1, 4, 28, 2, 1, 6, 2, 10, 3, 1, 2, 2
Offset: 0

Views

Author

Benoit Cloitre, Nov 29 2002

Keywords

Links

Crossrefs

Cf. A073009 (decimal expansion).

Programs

  • PARI
    default(realprecision, 10^5); contfrac(suminf(k=1, k^-k)) \\ Jinyuan Wang, Mar 04 2020

Extensions

Offset changed by Andrew Howroyd, Aug 07 2024

A100084 Decimal expansion of Sum_{n>0} 1/(n^(n!)).

Original entry on oeis.org

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

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 08 2004

Keywords

Examples

			1.251371742112486405937272764835634431067154077181927...

Crossrefs

Cf. A073009, A099870 to A099873.

Programs

  • PARI
    sum(n=1,9,1/(n^(n!)),0.)

A134881 Decimal expansion of Sum_{k>=1} 1/(e^k)^(e^k).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Nov 14 2007

Keywords

Examples

			0.06598841774334379175656238672410779743814443934121...

Crossrefs

Cf. A073009, A100085, A134877, A134878, A134879, A134890.

Programs

  • Mathematica
    RealDigits[N[Sum[1/(E^n)^(E^n), {n, 1, 20}], 200]][[1]] (* first two zeros removed *)

A215578 Decimal expansion of Sum_{n>=1} 1/n^(n^n).

Original entry on oeis.org

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

Views

Author

Balarka Sen, Aug 16 2012

Keywords

Comments

A more general function is L(z) = sum(n=1,Infinity,1/n^^z).
What is the value of L(4)?
L(4) = 1.0000152587890625000... where the next 3 trillion decimal places are 0. - Charles R Greathouse IV, Sep 20 2012

Examples

			1.062500000000131137265239709250723468551954313530249 . . .

Links

Crossrefs

Cf. A073009, A002488.

Programs

  • PARI
    suminf(n=1,1/n^(n^n))

A258102 Decimal expansion of Sum_{k >= 1} k^(-k^2).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, May 20 2015

Keywords

Examples

			1.06255080549625593786944593879337586328548415733862632010781...

Links

Crossrefs

Cf. A073009.

Programs

  • Maple
    evalf(Sum(k^(-k^2), k=1..infinity), 120); # Vaclav Kotesovec, May 21 2015
  • Mathematica
    NSum[k^(-k^2), {k, 1, Infinity}, WorkingPrecision -> 105] // RealDigits // First
  • PARI
    default(realprecision,120); sumpos(k=1, k^(-k^2)) \\ Vaclav Kotesovec, May 21 2015

A336284 Decimal expansion of Sum_{n>=2} n^(log(n))/log(n)^n.

Original entry on oeis.org

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

Views

Author

Bernard Schott, Jul 17 2020

Keywords

Comments

This series is convergent because there exists n_1 such that for n >= n_1, n^(log(n))/log(n)^n <= (1/sqrt(e))^n.

Examples

			10.5417051152289715912697153360630929474717489965883...

Crossrefs

Cf. A073009 (1/n^n), A099870 (1/n^log(n)), A099871 (1/log(n)^n), A308915 (1/(log(n)^log(n))).
Cf. A092605 (1/sqrt(e)).

Programs

  • Maple
    evalf(sum(n^(log(n))/log(n)^n, n=2..infinity),100);
  • PARI
    suminf(n=2, n^(log(n))/log(n)^n) \\ Michel Marcus, Jul 17 2020

Formula

Equals Sum_{n>=2} n^(log(n))/log(n)^n.

A338168 Decimal expansion of Sum_{n>=1} 1/(2n-1)^(2n).

Original entry on oeis.org

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

Views

Author

Mario Cortés, Oct 14 2020

Keywords

Comments

This is the sum of the inverse of odd numbers raised to the even numbers.

Examples

			1.0124098527659873204681857270193548770717264307070789173009...

Crossrefs

Cf. A073009, A222621, A338167.

Programs

  • PARI
    suminf(n=1, (2*n-1)^(-2*n))

Formula

Equals Sum_{n>=1} 1/A222621(n).
Previous Showing 21-30 of 49 results. Next

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