A179407 -id:A179407 - cp's OEIS frontend

A179408 Values y for records of minima of positive distance d between a fifth power of a positive integer x and a square of an integer y such d = x^5 - y^2 (x != k^2 and y != k^5).

181, 22434, 50354, 2759646, 3834168, 5562261, 10980023, 18329057, 142674503, 2093555387, 12135618855, 29588700403, 72673092233, 423129175811, 425213412449, 2855547523353, 482836315990072, 484925830443335

Offset: 1

Artur Jasinski, Jul 13 2010

Distance d is equal to 0 when x = k^2 and y = k^5.
For d values, see A179406.
For x values, see A179407.
Conjecture (from Artur Jasinski):
For any positive number x >= A179407(n), the distance d between fifth power of x and the square of any y (such that x != k^2 and y != k^5) can't be less than A179406(n).

J. Blass, A Note on Diophantine Equation Y^2 + k = X^5, Math. Comp. 1976, Vol. 30, No. 135, pp. 638-640.
A. Bremner, On the Equation Y^2 = X^5 + k, Experimental Mathematics 2008 Vol. 17, No. 3, pp. 371-374.

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179406, A179407.

max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^5)^(1/2)]; k = n^5 - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 96001}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy (* Artur Jasinski, Jul 13 2010 *)

A179407(n)^5-a(n)^2 = A179406(n).

A179784 Records for minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

Original entry on oeis.org

7, 71, 95, 448, 1756, 2215, 3983, 6271, 15231, 26775, 26870, 57475, 102703, 221916, 257963, 9053750, 9297464, 9321703, 27188154, 48787589, 62396287, 83146412, 152244535, 44475611670, 74378479183, 179884971502, 929051699593

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^7.
For x values see A179785.
For y values see A179786.
Conjecture (Artur Jasinski): For any positive number x >= A179785(n), the distance d between the seventh power of x and the square of any y (such that x <> k^2 and y <> k^7) can't be less than A179784(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179785, A179786.

d = 7; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd

A179785 Values x for records of minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

Original entry on oeis.org

2, 3, 6, 8, 10, 14, 18, 20, 28, 30, 39, 55, 59, 88, 239, 255, 257, 374, 387, 477, 1136, 1221, 9104, 10959, 35962, 43783, 96569, 148544, 183163, 194933, 313592, 842163, 1254392, 1468637, 1506412, 2377393, 2407523, 4636475, 5756417, 6615968

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^7.
For d values see A179784.
For y values see A179786.
Conjecture (Artur Jasinski): For any positive number x >= A179785(n), the distance d between the seventh power of x and the square of any y (such that x <> k^2 and y <> k^7) can't be less than A179784(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179786.

d = 7; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; xx

A179786 Values y for records of the minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

Original entry on oeis.org

11, 46, 529, 1448, 3162, 10267, 24743, 35777, 116159, 147885, 370447, 1233870, 1577546, 6392774, 211053546, 264783325, 272123427, 1011697339, 1140219273, 2370360092, 49411058753, 63606986977, 71996746561757, 137783827309893

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^7.
For d values see A179784.
For x values see A179785.
Conjecture (Artur Jasinski): For any positive number x >= A179785(n), the distance d between the seventh power of x and the square of any y (such that x <> k^2 and y <> k^7) can't be less than A179784(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785.

d = 7; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy

A179790 Records for minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

Original entry on oeis.org

28, 83, 1516, 3420, 5503, 30889, 75228, 776563, 2428283, 3035356, 29901479, 68334642, 113284785, 776887258, 1719856432, 3353407292, 19232010711, 27678166236, 29160146546, 305337557432, 95950163566107, 114852386371373

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^9.
For x values see A179791.
For y values see A179792.
Conjecture (Artur Jasinski): For any positive number x >= A179791(n), the distance d between the ninth power of x and the square of any y (such that x <> k^2 and y <> k^9) can't be less than A179790(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 9; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd

A179791 Values x for records of the minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

Original entry on oeis.org

2, 3, 5, 6, 8, 13, 22, 23, 27, 62, 78, 147, 181, 203, 233, 468, 892, 1110, 1827, 3657, 3723, 10637, 11145, 11478, 12275, 16764, 19151, 22719, 23580, 24974, 30163, 36885, 41759, 41948, 44427, 66443, 86167, 96658, 115992, 222962, 248461, 248588, 384573

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^9.
For d values see A179790.
For y values see A179792.
Conjecture (Artur Jasinski): For any positive number x >= A179791(n), the distance d between the ninth power of x and the square of any y (such that x <> k^2 and y <> k^9) can't be less than A179790(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 9; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; xx

A179792 Values y for records of the minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

Original entry on oeis.org

22, 140, 1397, 3174, 11585, 102978, 1098758, 1342070, 2761448, 116348986, 326908123, 5661454305, 14439547606, 24195364585, 44988513611, 1037782490126, 18907836782131, 50577039498042, 476237361126871, 10815891488601655

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^9.
For d values see A179790.
For x values see A179791.
Conjecture (Artur Jasinski): For any positive number x >= A179791(n), the distance d between the ninth power of x and the square of any y (such that x <> k^2 and y <> k^9) can't be less than A179790(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 9; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy

A179793 Records of minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

Original entry on oeis.org

23, 747, 8847, 12654, 166831, 484471, 573055, 1248668, 1602775, 8764352, 72820023, 94338007, 143404871, 155195023, 262310000, 1529935249, 4884962400, 19571071932, 146228748359, 318603821009, 635586109888, 1305633968055

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^11.
For x values see A179794.
For x values see A179795.
Conjecture (Artur Jasinski): For any positive number x >= A179794(n), the distance d between the eleventh power of x and the square of any y (such that x <> k^2 and y <> k^11) can't be less than A179793(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 11; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd

A179794 Values x for records of the minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

Original entry on oeis.org

2, 3, 6, 7, 8, 10, 14, 18, 20, 26, 28, 32, 38, 52, 60, 77, 145, 168, 222, 237, 268, 279, 286, 359, 367, 390, 536, 569, 622, 872, 1085, 1349, 1462, 1760, 1932, 2423, 2801, 5559, 5925, 7052, 8383, 8752, 10075, 11917, 15712, 17420, 17598, 23712, 26026, 28095

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^11.
For x values see A179794.
For x values see A179795.
Conjecture (Artur Jasinski): For any positive number x >= A179794(n), the distance d between the eleventh power of x and the square of any y (such that x <> k^2 and y <> k^11) can't be less than A179793(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 11; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; xx

A179795 Values y for records of the minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

Original entry on oeis.org

45, 420, 19047, 44467, 92681, 316227, 2012353, 8016758, 14310835, 60583368, 91068707, 189812531, 488438379, 2741690265, 6023263700, 23751934582, 771834189385, 1734606819630, 8034176335637, 11511075516802, 22632960587688

Offset: 1

Artur Jasinski, Jul 27 2010

nonn

Distance d is equal to 0 when x = k^2 and y = k^11.
For x values see A179794.
For x values see A179795.
Conjecture (Artur Jasinski):
For any positive number x >= A179794(n), the distance d between the eleventh power of x and the square of any y (such that x <> k^2 and y <> k^11) can't be less than A179793(n).

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.

d = 11; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy

cp's OEIS Frontend

A179408 Values y for records of minima of positive distance d between a fifth power of a positive integer x and a square of an integer y such d = x^5 - y^2 (x != k^2 and y != k^5).

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A179784 Records for minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

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A179785 Values x for records of minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

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A179786 Values y for records of the minima of the positive distance d between the seventh power of a positive integer x and the square of an integer y such that d = x^7 - y^2 (x <> k^2 and y <> k^7).

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A179790 Records for minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

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A179791 Values x for records of the minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

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A179792 Values y for records of the minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

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A179793 Records of minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

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A179794 Values x for records of the minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

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A179795 Values y for records of the minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).

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