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 1-6 of 6 results.

A242760 Decimal expansion of the odd limit of the harmonic power tower (1/2)^(1/3)^...^(1/(2n+1)).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, May 22 2014

Keywords

Comments

The harmonic power tower sequence is divergent in the sense that even and odd partial exponentials converge to distinct limits. [after Steven Finch]

Examples

			0.6903471261149643194673284384641894244398...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.11, p. 449.

Links

Crossrefs

Cf. A242759.

Programs

  • Mathematica
    digits = 40; dn = 10; $RecursionLimit = 1000; Clear[h]; h[n_] := h[n] = Power @@ (1/Range[2, n]); h[dn + 1]; h[n = 2*dn + 1]; While[RealDigits[h[n], 10, digits] != RealDigits[h[n - dn], 10, digits], Print["n = ", n]; n = n + dn]; RealDigits[h[n], 10, digits] // First
digits = 120; difs = 1; sold = 0; n = 100; While[Abs[difs] > 10^(-digits - 5), s = N[1/(2*n + 1), 1000]; Do[s = 1/m^s, {m, 2*n, 2, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Feb 17 2021 *)

Extensions

More terms from Alois P. Heinz, May 22 2014

A102575 Decimal expansion of 2^(3/2)^(4/3)^(5/4)^(6/5)^(7/6)^(8/7)^(9/8)^(10/9)^(11/10)....

Original entry on oeis.org

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

Views

Author

Raes Tom (tommy1729(AT)hotmail.com), Feb 25 2005

Keywords

Comments

I do not use brackets for the powers, so do not confuse this with 2^(3/2*4/3*5/4...)
Obtaining 100 digits of precision only requires computing 2^(3/2)^(4/3)^...^(70/69). - Ryan Propper, May 06 2006

Examples

			3.5038099724520171086395374917713267007683... - _Jianing Song_, Nov 18 2018

Crossrefs

Cf. A242759, A242760, A341324, A341325.

Programs

  • Mathematica
    k = 1; For[a = 100, a > 1, a--, k = (a/(a-1))^k]; First[RealDigits[N[k, 100]]] (* Ryan Propper, May 06 2006 *)

Extensions

More terms from Ryan Propper, May 06 2006

A341324 Decimal expansion of (1/4)^(4/9)^...^(n^2/(n+1)^2)^... .

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Feb 08 2021

Keywords

Examples

			0.4449047137975709943818158062572891757596036582203842557173...

Crossrefs

Cf. A242759, A242760, A341325.

Programs

  • Mathematica
    digits = 120; difs = 1; sold = 0; n = 10; While[Abs[difs] > 10^(-digits - 5), s = N[n^2/(n + 1)^2, 1000]; Do[s = (m^2/(m + 1)^2)^s, {m, n - 1, 1, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Feb 17 2021 *)

Extensions

More digits from Alois P. Heinz, Feb 16 2021

A341325 Decimal expansion of (1/2)^(2/3)^...^(n/(n+1))^... .

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Feb 08 2021

Keywords

Examples

			0.604407600444447842412203840443406857098633311299855...

Crossrefs

Cf. A242759, A242760, A341324.

Programs

  • Mathematica
    digits = 120; difs = 1; sold = 0; n = 10; While[Abs[difs] > 10^(-digits - 5), s = N[n/(n + 1), 1000]; Do[s = (m/(m + 1))^s, {m, n - 1, 1, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Feb 17 2021 *)

Extensions

More digits from Alois P. Heinz, Feb 16 2021

A339099 Decimal expansion of (2/1)^(5/4)^...^((n^2+1)/n^2)^... .

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Feb 21 2021

Keywords

Examples

			2.434406112635718027389325512218569477657688308056714... .

Crossrefs

Cf. A341324, A341325, A242759, A242760, A102575

Extensions

More digits from Alois P. Heinz, Feb 21 2021

A341863 Decimal expansion of (4/1)^(9/4)^...^((n+1)^2/n^2)^... .

Original entry on oeis.org

4, 4, 1, 7, 6, 3, 4, 7, 7, 9, 0, 3, 6, 2, 3, 0, 4, 3, 7, 4, 1, 9, 0, 4, 6, 0, 0, 9, 0, 6, 3, 5, 4, 7, 7, 6, 6, 9, 9, 9, 2, 7, 5, 4, 3, 3, 0, 4, 5, 8, 7, 1, 3, 3, 1, 7, 6, 0, 0, 6, 3, 4, 0, 3, 2, 3, 5, 9, 9, 2, 2, 6, 9, 2, 8, 5, 9, 1, 9, 4, 2, 8, 3, 3, 3, 4, 7, 7, 4, 1, 1, 5, 6, 9, 8, 3, 7, 2, 1, 8, 7, 3, 1, 7, 3
Offset: 11

Views

Author

Koksal Karakus, Feb 21 2021

Keywords

Examples

			44176347790.3623043741904600906354776699927543304587133176...

Crossrefs

Cf. A341324, A341325, A242759, A242760, A102575.

Programs

  • Mathematica
    digits = 120; difs = 1; sold = 0; n = 10; While[Abs[difs] > 10^(-digits - 5), s = N[(n + 1)^2/n^2, 1000]; Do[s = ((m + 1)^2/m^2)^s, {m, n - 1, 1, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Mar 03 2021 *)

Extensions

More digits from Alois P. Heinz, Mar 02 2021
Showing 1-6 of 6 results.

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