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.

User: Koksal Karakus

Koksal Karakus's wiki page.

Koksal Karakus has authored 22 sequences. Here are the ten most recent ones:

A342201 Decimal expansion of Sum_{k>=1} (1 - (1/k)^(1/k^k)).

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Mar 04 2021

Keywords

Examples

			0.204932591462...

Crossrefs

Cf. A342200.

Programs

  • PARI
    suminf(k=1, 1 - (1/k)^(1/k^k)) \\ Michel Marcus, Mar 05 2021

Extensions

More digits from Alois P. Heinz, Mar 05 2021

A342200 Decimal expansion of Product_{k>=1} (1/k)^(1/k^k).

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Mar 04 2021

Keywords

Examples

			0.802561117519...

Crossrefs

Cf. A342201.

Programs

Extensions

More digits from Alois P. Heinz, Mar 05 2021

A342220 Decimal expansion of solution to zeta(x) = Pi.

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Mar 05 2021

Keywords

Examples

			zeta(1.39425321984488839...) = Pi.

Crossrefs

Cf. A000796 (Pi), A107311, A342203.

Programs

  • Mathematica
    RealDigits[x /. FindRoot[Zeta[x] - Pi, {x, 2}, WorkingPrecision -> 120], 10, 100][[1]] (* Amiram Eldar, May 31 2021 *)
  • PARI
    solve(x=1.1, 2, zeta(x) - Pi) \\ Michel Marcus, Mar 07 2021

Extensions

More terms from Jon E. Schoenfield, Mar 07 2021

A342203 Decimal expansion of solution to zeta(x) = e.

Original entry on oeis.org

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

Views

Author

Koksal Karakus, Mar 04 2021

Keywords

Examples

			zeta(1.4744642873...) = e.

Crossrefs

Cf. A001113 (e), A107311.

Programs

  • Mathematica
    RealDigits[x /. FindRoot[Zeta[x] == E, {x, 2}, WorkingPrecision -> 105], 10, 100][[1]] (* Amiram Eldar, Mar 05 2021 *)
  • PARI
    solve(x=1.1, 2, zeta(x)-exp(1)) \\ Michel Marcus, Mar 05 2021

Extensions

More digits from Alois P. Heinz, Mar 05 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

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

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

A071107 a(n) is the greatest integer that can be obtained from the integers {1, 2, 3, ..., n} using each number at most once and the operators +,-,*,/,^.

Original entry on oeis.org

1, 3, 27, 115792089237316195423570985008687907853269984665640564039457584007913129639936
Offset: 1

Views

Author

Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002

Keywords

Comments

a(4) = 2^(4^4) = 2^256 = 115792089237316195423570985008687907853269984665640564039457584007913129639936 with 78 digits. a(5) = 2^(3^(4^6)) with more than 10^1950 digits.

Examples

			a(3) = 27 because 3^(2+1) = 27 is the greatest integer that can be obtained by using 1, 2, 3 once and the operations +, -, *, /, ^.

Crossrefs

Cf. A070960.

A071794 a(n) is the smallest integer > 0 that cannot be obtained from the integers {1, ..., n} using each number at most once and the operators +, -, *, /, ^.

Original entry on oeis.org

2, 4, 11, 34, 178, 926, 9434
Offset: 1

Views

Author

Koksal Karakus (karakusk(AT)hotmail.com), Jun 06 2002

Keywords

Comments

The old entry a(6) = 791 was incorrect since 791 = (2^5 + 3^4) (1+6). - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007. Also 791 = ((3*5)^4-1)/2^6. - Sam Handler (shandler(AT)macalester.edu) and Kurt Bachtold (kbachtold(AT)route24.net), Feb 28 2007.
I believe that a(7) = 9434 (with approximately 98% certainty). - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
Using the Java programming language, my brother and I have independently created 2 programs which absolutely solve this problem for a given index via brute force algorithms. Our process is to systematically generate every possible equation in polish notation, solve it, then add its solution (providing that it is a positive integer) to a list of previous solutions. After all solutions have been calculated, the program references the list to find the lowest missing number. - Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007

Examples

			a(3)=11 because using {1,2,3} we can write 1, 2, 3, 3+1=4, 3+2=5, 3*2=6, 3*2+1=7, 2^3=8, 3^2=9, (3^2)+1=10 but we cannot obtain 11 in the same way.

References

  • B. Torrence, Arithmetic Combinations, Mathematica in Education and Research, Vol. 12, No. 1 (2007), pp. 47-59.

Links

Crossrefs

Cf. A060315.

Programs

  • Mathematica
    The Torrence article gives a description of how one can use Mathematica to investigate the sequence.

Extensions

a(6) corrected by Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
a(7) from Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007

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