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 1-10 of 28 results. Next

A173348 Numbers x such that 0 < |x^7 - y^2| < x^(5/2) for some number y.

Original entry on oeis.org

12, 93, 239, 4896, 4904, 6546, 7806, 9104, 20542, 35962, 43783, 96569, 616400, 635331, 842163, 7888432, 450177181
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

Beukers and Stewart conjecture that for coprime integers n and m with n > m >= 2, and for any c > 0, the inequality 0 < |x^n - y^m| < c*X^(1-1/n-1/m) is true for infinitely many positive integers x and y, where X = max(x^n,y^m). They compute such x for 34 pairs (n,m). Given x, it is easy to compute y = round(x^(n/m)). Their tables have been extended to include all terms < 10^7 (or higher to obtain more terms).
a(18) > 10^9. - Robert Price, Apr 15 2021

Links

  • F. Beukers and C. L. Stewart, Neighboring powers, J. Number Theory, 130 (2010), 660-679.

Crossrefs

Cf. A078933 (m=2, n=3, Hall's conjecture)
Cf. A116884 (m=2, n=5)
This sequence (m=2, n=7)
Cf. A173349 (m=2, n=9)
Cf. A173350 (m=2, n=11)
Cf. A173351 (m=3, n=4)
Cf. A173352 (m=3, n=5)
Cf. A173353 (m=3, n=7)
Cf. A173354 (m=3, n=8)
Cf. A173355 (m=3, n=10)
Cf. A173356 (m=3, n=11)
Cf. A173357 (m=4, n=5)
Cf. A173358 (m=4, n=7)
Cf. A173359 (m=4, n=9)
Cf. A173360 (m=4, n=11)
Cf. A173361 (m=5, n=6)
Cf. A173362 (m=5, n=7)
Cf. A173363 (m=5, n=8)
Cf. A173364 (m=5, n=9)
Cf. A173365 (m=5, n=11)
Cf. A173366 (m=5, n=12)
Cf. A173367 (m=6, n=7)
Cf. A173368 (m=6, n=11)
Cf. A173369 (m=7, n=8)
Cf. A173370 (m=7, n=9)
Cf. A173371 (m=7, n=10)
Cf. A173372 (m=7, n=11)
Cf. A173373 (m=7, n=12)
Cf. A173374 (m=8, n=9)
Cf. A173375 (m=8, n=11)
Cf. A173376 (m=9, n=10)
Cf. A173377 (m=9, n=11)
Cf. A173378 (m=10, n=11)
Cf. A173379 (m=11, n=12)

Programs

  • Mathematica
    Solutions[n_,m_,lim_] := Module[{x, y, t={}, pow=n*(1-1/m-1/n)}, Do[y=Round[x^(n/m)]; If[0 < Abs[x^n-y^m]

Extensions

a(17) from Robert Price, Apr 15 2021

A116885 Integers n such that 0<|n^5-m^2|<= n for some integer m.

Original entry on oeis.org

1, 8, 55, 76, 377
Offset: 1

Views

Author

Giovanni Resta, Feb 27 2006

Keywords

Comments

Next term, if any, must be greater than 50*10^9.

Examples

			|377^5-2759646^2| = 341 <= 377.

Crossrefs

Cf. A078933, A116884.

A173352 Numbers x such that 0 < |x^5 - y^3| < x^(7/3) for some number y.

Original entry on oeis.org

2, 4, 23, 122, 199, 408, 4995, 7320, 44217, 177682, 394826, 1706886, 1738064, 8403388, 21194961, 110525339, 314033376, 328840890
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(19) > 10^9. - Robert Price, Apr 18 2021

Crossrefs

Cf. A173341 (n^5 and a cube are between consecutive squares)
Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[5,3,10^7] (* see A173348 *)

Extensions

a(15)-a(18) from Robert Price, Apr 18 2021

A173353 Numbers x such that 0 < |x^7 - y^3| < x^(11/3) for some number y.

Original entry on oeis.org

2, 3, 32, 33, 34, 88, 442, 498, 942, 2266144, 12527271, 20160899, 272585923
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(14) > 10^9. - Robert Price, Apr 20 2021

Crossrefs

Cf. A173342 (n^7 and a cube are between consecutive squares)
Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[7,3,10^7] (* see A173348 *)

Extensions

a(11)-a(13) from Robert Price, Apr 20 2021

A173354 Numbers x such that 0 < |x^8 - y^3| < x^(13/3) for some number y.

Original entry on oeis.org

97, 37840, 199652, 2905727, 24052021, 60388240, 121585856, 175214594
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

See A173348 for more information.
a(9) > 10^9. - Robert Price, Apr 21 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[8,3,10^7] (* see A173348 *)

Extensions

a(5)-a(8) from Robert Price, Apr 21 2021

A173355 Numbers x such that 0 < |x^10 - y^3| < x^(17/3) for some number y.

Original entry on oeis.org

2, 3, 48, 73, 436, 23494, 37381, 621706, 781913, 2351612, 49301348, 96493921, 141630007
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(14) > 10^9. - Robert Price, Apr 25 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[10,3,10^7] (* see A173348 *)

Extensions

a(11)-a(13) from Robert Price, Apr 25 2021

A173356 Numbers x such that 0 < |x^11 - y^3| < x^(19/3) for some number y.

Original entry on oeis.org

82, 858, 28439, 166378, 174879, 977170, 1330997, 1595395, 3393037, 5699501, 7815232, 12258613, 14243561, 16779169, 681471994
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(16) > 10^9. - Robert Price, Apr 26 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[11,3,10^7] (* see A173348 *)

Extensions

a(12)-a(15) from Robert Price, Apr 26 2021

A173357 Numbers x such that 0 < |x^5 - y^4| < x^(11/4) for some number y.

Original entry on oeis.org

3, 53, 7702, 10836, 11944, 338295, 422295, 857745, 106705488, 571424506
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(11) > 10^9. - Robert Price, Apr 28 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[5,4,10^7] (* see A173348 *)

Extensions

a(9)-a(10) from Robert Price, Apr 28 2021

A173358 Numbers x such that 0 < |x^7 - y^4| < x^(17/4) for some number y.

Original entry on oeis.org

6, 13, 21, 59, 3053, 7075, 8509, 168511, 1413693, 13146901
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(11) > 10^9. - Robert Price, May 01 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[7,4,10^7] (* see A173348 *)

Extensions

a(10) from Robert Price, May 01 2021

A173359 Numbers x such that 0 < |x^9 - y^4| < x^(23/4) for some number y.

Original entry on oeis.org

12, 127, 3137, 208870, 298574, 6805600, 157457247
Offset: 1

Views

Author

T. D. Noe, Feb 22 2010

Keywords

Comments

No additional terms < 10^7. See A173348 for more information.
a(8) > 10^9. - Robert Price, May 01 2021

Crossrefs

Cf. A078933, A116884, A173348-A173379.

Programs

  • Mathematica
    Solutions[9,4,10^7] (* see A173348 *)

Extensions

a(7) from Robert Price, May 01 2021
Showing 1-10 of 28 results. Next

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