A078933 -id:A078933 - cp's OEIS frontend

A173373 Numbers x such that 0 < |x^12 - y^7| < x^(65/7) for some number y.

Original entry on oeis.org

11, 39, 163, 876, 259632, 310504, 1521835

Offset: 1

T. D. Noe, Feb 22 2010

nonn

See A173348 for more information.

a(8) > 10^9. - Robert Price, May 30 2021

Cf. A078933, A116884, A173348-A173379.

Mathematica
```
Solutions[12,7,10^7] (* see A173348 *)
```

A173374 Numbers x such that 0 < |x^9 - y^8| < x^(55/8) for some number y.

Original entry on oeis.org

426, 9807, 84332, 91524247

Offset: 1

T. D. Noe, Feb 22 2010

No additional terms < 10^7. See A173348 for more information.

a(5) > 10^9. - Robert Price, May 31 2021

Cf. A078933, A116884, A173348-A173379.

Mathematica
```
Solutions[9,8,10^7] (* see A173348 *)
```

a(4) from Robert Price, May 31 2021

A173375 Numbers x such that 0 < |x^11 - y^8| < x^(69/8) for some number y.

Original entry on oeis.org

177, 11266, 115871

Offset: 1

T. D. Noe, Feb 22 2010

No additional terms < 10^7. See A173348 for more information.

a(4) > 10^9. - Robert Price, Jun 02 2021

Cf. A078933, A116884, A173348-A173379.

Mathematica
```
Solutions[11,8,10^7] (* see A173348 *)
```

A173376 Numbers x such that 0 < |x^10 - y^9| < x^(71/9) for some number y.

Original entry on oeis.org

5, 44, 133, 3550208

Offset: 1

T. D. Noe, Feb 22 2010

See A173348 for more information.

a(5) > 10^9. - Robert Price, Jun 04 2021

Cf. A078933, A116884, A173348-A173379.

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

A173377 Numbers x such that 0 < |x^11 - y^9| < x^(79/9) for some number y.

Original entry on oeis.org

55, 706

Offset: 1

T. D. Noe, Feb 22 2010

See A173348 for more information.

a(3) > 10^9. - Robert Price, Jun 06 2021

Cf. A078933, A116884, A173348-A173379.

Mathematica
```
Solutions[11,9,10^8] (* see A173348 *)
```

A173378 Numbers x such that 0 < |x^11 - y^10| < x^(89/10) for some number y.

Original entry on oeis.org

20598, 125496, 681143, 803178, 236887630

Offset: 1

T. D. Noe, Feb 22 2010

No additional terms < 10^7. See A173348 for more information.

a(6) > 10^9. - Robert Price, Jun 07 2021

Cf. A078933, A116884, A173348-A173379.

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

a(5) from Robert Price, Jun 07 2021

A380405 Squares k such that there are no primes between k and the nearest cube that is not k.

Original entry on oeis.org

9, 25, 121, 32761, 79524, 97344

Offset: 1

Zhining Yang, Jan 26 2025

There are no other terms < 2*10^30.

			121 is a term because it is a square and there are no primes between 123 and 125, its nearest cube.

Cf. A053706, A380521, A380522, A380523, A078933.

b[n_] := If[IntegerQ@Sqrt@n, 0, p = NextPrime[n^3];
  q = Ceiling[Sqrt[NextPrime[p, -1]]];  If[q^2 >= p, 0, q]];
 Select[Array[b@# &, 1000], # > 0 &]^2

A198831 Successive records in maximal positive distance d = x^3 - y^2.

Original entry on oeis.org

0, 4, 20, 28, 39, 47, 81, 135, 152, 207, 216, 270, 496, 546, 615, 732, 832, 1148, 1208, 1343, 1391, 1541, 1750, 2000, 2260, 2548, 2575, 2825, 3679, 3807, 4220, 4604, 5076, 5508, 5835, 5859, 6291, 7538, 7656, 8188, 8423, 8712, 8964, 12092, 12205, 12511, 12926

Offset: 1

Artur Jasinski, Oct 30 2011

nonn

Successive records in A077116.

J. Calvo, J. Herranz, G. Saez, A new algorithm to search for small nonzero |x^3 - y^2| values, Math. Comp. 78 (2009), 2435-2444.

Cf. A077116, A078933, A179107, A179108, A179109.

aa = {}; bb = {}; max = -1; Do[kk = x^3 - Floor[x^(3/2)]^2; If[kk > max, AppendTo[aa, kk]; AppendTo[bb, x]; max = kk], {x, 1, 10000}]; aa

A198832 Values x for records of maxima of positive distance d between a cube of positive integer x and a square of integer y and such that d = x^3 - y^2.

Original entry on oeis.org

1, 2, 6, 8, 10, 12, 13, 19, 26, 31, 33, 39, 40, 43, 46, 52, 68, 72, 78, 84, 90, 93, 95, 105, 109, 133, 139, 149, 152, 162, 176, 180, 190, 202, 211, 219, 231, 243, 265, 269, 272, 306, 330, 336, 341, 346, 351, 356, 366, 393, 407, 422, 436, 446, 450, 467, 501

Offset: 1

Artur Jasinski, Oct 30 2011

nonn

J. Calvo, J. Herranz, G. Saez, A new algorithm to search for small nonzero |x^3 - y^2| values, Math. Comp. 78 (2009), 2435-2444.

Cf. A078933, A179107, A179108, A179109.

aa = {}; bb = {}; max = -1; Do[kk = x^3 - Floor[x^(3/2)]^2; If[kk > max, AppendTo[aa, kk]; AppendTo[bb, x]; max = kk], {x, 1, 10000}]; bb

Definition modified by Harvey P. Dale, Sep 25 2019

A273927 Absolute difference between A000290(n) and the nearest term of A000578.

Original entry on oeis.org

1, 3, 1, 8, 2, 9, 15, 37, 17, 25, 4, 19, 44, 20, 9, 40, 54, 19, 18, 57, 71, 28, 17, 64, 104, 53, 217, 55, 112, 100, 39, 24, 89, 156, 106, 35, 38, 113, 190, 128, 47, 36, 121, 208, 172, 81, 12, 107, 204, 244, 143, 40, 65, 172, 281, 239, 126, 11, 106, 225, 346

Offset: 1

Felix Fröhlich, Jun 04 2016

nonn

Marshall Hall, Jr. conjectured that there exists a constant c > 0 such that for any integers x and y with y^2 != x^3 the relation abs(y^2 - x^3) > c*sqrt(abs(x)) holds.

Wikipedia, Hall's conjecture.

Cf. A078933, A199496, A199497, A199498.

nearestcube(n) = my(x=n-1, y=n+1); while(!ispower(x, 3) && !ispower(y, 3), x--; y++); if(ispower(x, 3), return(x)); if(ispower(y, 3), return(y))
a(n) = abs(n^2 - nearestcube(n^2))

cp's OEIS Frontend

A173373 Numbers x such that 0 < |x^12 - y^7| < x^(65/7) for some number y.

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A173374 Numbers x such that 0 < |x^9 - y^8| < x^(55/8) for some number y.

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A173375 Numbers x such that 0 < |x^11 - y^8| < x^(69/8) for some number y.

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A173376 Numbers x such that 0 < |x^10 - y^9| < x^(71/9) for some number y.

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Mathematica

A173377 Numbers x such that 0 < |x^11 - y^9| < x^(79/9) for some number y.

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A173378 Numbers x such that 0 < |x^11 - y^10| < x^(89/10) for some number y.

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Mathematica

Extensions

A380405 Squares k such that there are no primes between k and the nearest cube that is not k.

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A198831 Successive records in maximal positive distance d = x^3 - y^2.

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Mathematica

A198832 Values x for records of maxima of positive distance d between a cube of positive integer x and a square of integer y and such that d = x^3 - y^2.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A273927 Absolute difference between A000290(n) and the nearest term of A000578.

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