A257416 -id:A257416 - cp's OEIS frontend

A257411 Values of n such that there are exactly 4 solutions to x^2 - y^2 = n with x > y >= 0.

96, 105, 120, 135, 160, 165, 168, 189, 195, 216, 224, 231, 255, 256, 264, 273, 280, 285, 297, 312, 345, 351, 352, 357, 375, 385, 399, 408, 416, 420, 429, 435, 440, 455, 456, 459, 465, 483, 512, 513, 520, 540, 544, 552, 555, 561, 595, 608, 609, 615, 616, 621

Offset: 1

Colin Barker, Apr 22 2015

nonn

			96 is in the sequence because there are 4 solutions to x^2 - y^2 = 96, namely (x,y) = (10,2), (11,5), (14,10), (25,23).

Colin Barker, Table of n, a(n) for n = 1..600

Cf. A257408, A257409, A257410, A257412, A257413, A257414, A257415, A257416, A257417.

Cf. A034178.

nn = 1000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 4] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257411(n)={A034178(n)==4} \\ M. F. Hasler, Apr 22 2015

A257417 Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.

Original entry on oeis.org

960, 1344, 1728, 2112, 2240, 2496, 2592, 2835, 3240, 3264, 3520, 3648, 4160, 4416, 4455, 4536, 4928, 5265, 5440, 5568, 5824, 5952, 6080, 6144, 6237, 6885, 7104, 7128, 7360, 7371, 7616, 7695, 7872, 8000, 8256, 8424, 8512, 9024, 9152, 9280, 9315, 9639, 9920

Offset: 1

Colin Barker, Apr 22 2015

nonn

			960 is in the sequence because there are 10 solutions to x^2 - y^2 = 960, namely (x,y) = (31,1), (32,8), (34,14), (38,22), (46,34), (53,43), (64,56), (83,77), (122,118), (241,239).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 200 terms from Colin Barker)

Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257415, A257416.

Cf. A034178.

nn = 10000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 10] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257417(n)={A034178(n)==10} \\ M. F. Hasler, Apr 22 2015

A257412 Values of n such that there are exactly 5 solutions to x^2 - y^2 = n with x > y >= 0.

Original entry on oeis.org

144, 192, 225, 320, 400, 405, 441, 448, 567, 648, 704, 784, 832, 891, 900, 1024, 1053, 1088, 1089, 1216, 1225, 1377, 1472, 1521, 1539, 1620, 1764, 1856, 1863, 1875, 1936, 1984, 2048, 2268, 2349, 2368, 2511, 2601, 2624, 2704, 2752, 2997, 3008, 3025, 3249

Offset: 1

Colin Barker, Apr 22 2015

nonn

			144 is in the sequence because there are 5 solutions to x^2 - y^2 = 144, namely (x,y) = (12,0), (13,5), (15,9), (20,16), (37,35).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 150 terms from Colin Barker)

Cf. A257408, A257409, A257410, A257411, A257413, A257414, A257415, A257416, A257417.

Cf. A034178.

nn = 4000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 5] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257412(n)={A034178(n)==5} \\ M. F. Hasler, Apr 22 2015

A257413 Values of n such that there are exactly 6 solutions to x^2 - y^2 = n with x > y >= 0.

Original entry on oeis.org

240, 288, 315, 336, 360, 384, 432, 495, 504, 525, 528, 560, 585, 600, 624, 640, 675, 693, 735, 765, 792, 800, 816, 819, 825, 855, 880, 896, 912, 936, 975, 1035, 1040, 1071, 1104, 1125, 1176, 1197, 1215, 1224, 1232, 1260, 1275, 1287, 1305, 1323, 1360, 1368

Offset: 1

Colin Barker, Apr 22 2015

nonn

			240 is in the sequence because there are 6 solutions to x^2 - y^2 = 240, namely (x,y) = (16,4), (17,7), (19,11), (23,17), (32,28), (61,59).

Colin Barker, Table of n, a(n) for n = 1..1100

Cf. A257408, A257409, A257410, A257411, A257412, A257414, A257415, A257416, A257417.

Cf. A034178.

nn = 2000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 6] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257413(n)={A034178(n)==6} \\ M. F. Hasler, Apr 22 2015

A257414 Values of n such that there are exactly 7 solutions to x^2 - y^2 = n with x > y >= 0.

Original entry on oeis.org

768, 1280, 1792, 2816, 3328, 3645, 4352, 4864, 5103, 5832, 5888, 7424, 7936, 8019, 9472, 9477, 10496, 11008, 12032, 12393, 13568, 13851, 14580, 15104, 15616, 16384, 16767, 17152, 18176, 18688, 20224, 20412, 21141, 21248, 22599, 22784, 24832, 25856, 26368

Offset: 1

Colin Barker, Apr 22 2015

nonn

			768 is in the sequence because there are 7 solutions to x^2 - y^2 = 768, namely (x,y) = (28,4), (32,16), (38,26), (52,44), (67,61), (98,94), (193,191).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 120 terms from Colin Barker)

Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257415, A257416, A257417.

Cf. A034178, A068314.

nn = 30000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 7] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257414(n)={A034178(n)==7} \\ M. F. Hasler, Apr 22 2015

A257415 Values of n such that there are exactly 8 solutions to x^2 - y^2 = n with x > y >= 0.

Original entry on oeis.org

480, 576, 672, 840, 864, 945, 1056, 1080, 1120, 1155, 1248, 1296, 1320, 1365, 1485, 1512, 1536, 1560, 1600, 1632, 1755, 1760, 1785, 1824, 1848, 1995, 2025, 2040, 2079, 2080, 2145, 2184, 2208, 2280, 2295, 2376, 2415, 2457, 2464, 2560, 2565, 2625, 2720, 2760

Offset: 1

Colin Barker, Apr 22 2015

nonn

			480 is in the sequence because there are 8 solutions to x^2 - y^2 = 480, namely (x,y) = (22,2), (23,7), (26,14), (29,19), (34,26), (43,37), (62,58), (121,119).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1600 terms from Colin Barker)

Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257416, A257417.

Cf. A034178.

nn = 3000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 8] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

is_A257415(n)={A034178(n)==8} \\ M. F. Hasler, Apr 22 2015

cp's OEIS Frontend

A257411 Values of n such that there are exactly 4 solutions to x^2 - y^2 = n with x > y >= 0.

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A257417 Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.

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A257412 Values of n such that there are exactly 5 solutions to x^2 - y^2 = n with x > y >= 0.

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A257413 Values of n such that there are exactly 6 solutions to x^2 - y^2 = n with x > y >= 0.

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A257414 Values of n such that there are exactly 7 solutions to x^2 - y^2 = n with x > y >= 0.

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Author

Keywords

Examples

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Crossrefs

Programs

Mathematica

PARI

A257415 Values of n such that there are exactly 8 solutions to x^2 - y^2 = n with x > y >= 0.

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Author

Keywords

Examples

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Programs

Mathematica

PARI