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Primes of the form x^2 + 45y^2.
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37
61, 109, 181, 229, 241, 349, 409, 421, 541, 601, 661, 709, 769, 829, 1009, 1021, 1069, 1129, 1201, 1249, 1321, 1381, 1429, 1489, 1549, 1609, 1621, 1669, 1741, 1789, 1801, 1861, 2029, 2089, 2161, 2221, 2269, 2281, 2341, 2389, 2521, 2689, 2749, 3001, 3049, 3061, 3109, 3121, 3169, 3181
Positive integers k such that x^2 - 8xy + y^2 + k = 0 has integer solutions.
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11
6, 11, 14, 15, 24, 35, 44, 51, 54, 56, 59, 60, 71, 86, 96, 99, 110, 119, 126, 131, 134, 135, 140, 150, 159, 176, 179, 191, 204, 206, 215, 216, 224, 231, 236, 239, 240, 251, 254, 275, 284, 294, 311, 315, 326, 335, 339, 344, 350, 359, 366, 371, 374, 375, 384
Primes of the form 2*x^2+6*x*y-3*y^2 (as well as of the form 5*x^2+10*x*y+2*y^2).
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10
2, 5, 17, 53, 113, 137, 173, 197, 233, 257, 293, 317, 353, 557, 593, 617, 653, 677, 773, 797, 857, 953, 977, 1013, 1097, 1193, 1217, 1277, 1373, 1433, 1493, 1553, 1613, 1637, 1697, 1733, 1877, 1913, 1973, 1997, 2153, 2213, 2237, 2273, 2297, 2333, 2357, 2393, 2417, 2477
Primes of the form -2*x^2+6*x*y+3*y^2 (as well as of the form 7*x^2+12*x*y+3*y^2).
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10
3, 7, 43, 67, 103, 127, 163, 223, 283, 307, 367, 463, 487, 523, 547, 607, 643, 727, 787, 823, 883, 907, 967, 1063, 1087, 1123, 1303, 1327, 1423, 1447, 1483, 1543, 1567, 1627, 1663, 1723, 1747, 1783, 1867, 1987, 2083, 2143, 2203, 2287, 2347, 2383, 2467, 2503, 2647, 2683
Primes of the form 3*x^2+16*y^2. Also primes of the form 4*x^2+4*x*y-5*y^2 (as well as primes the form 4*x^2+12*x*y+3*y^2).
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9
3, 19, 43, 67, 139, 163, 211, 283, 307, 331, 379, 499, 523, 547, 571, 619, 643, 691, 739, 787, 811, 859, 883, 907, 1051, 1123, 1171, 1291, 1459, 1483, 1531, 1579, 1627, 1699, 1723, 1747, 1867, 1987, 2011, 2083, 2131, 2179, 2203, 2251, 2347, 2371, 2467, 2539
Nonnegative numbers of the form 2x^2 + 6xy - 3y^2.
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3
0, 2, 5, 8, 17, 18, 20, 32, 33, 42, 45, 50, 53, 68, 72, 77, 80, 98, 105, 113, 122, 125, 128, 132, 137, 153, 162, 168, 170, 173, 177, 180, 197, 200, 212, 213, 218, 233, 242, 245, 257, 258, 272, 288, 293, 297, 305, 308, 317, 320, 330, 338, 353, 357, 362, 378
Nonnegative numbers of the form -2x^2+6xy+3y^2.
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3
0, 3, 7, 12, 22, 27, 28, 30, 43, 48, 55, 63, 67, 70, 75, 88, 102, 103, 108, 112, 118, 120, 127, 142, 147, 163, 172, 175, 183, 187, 192, 198, 220, 223, 238, 243, 252, 255, 262, 268, 270, 280, 283, 295, 300, 307, 318, 327, 343, 352, 355, 358, 363, 367, 382
Primes of the form 4*x^2 + 3*x*y - 4*y^2 (as well as of the form 2*x^2 + 9*x*y + y^2).
+10
2
2, 3, 19, 23, 37, 41, 61, 67, 71, 73, 79, 89, 97, 109, 127, 137, 149, 173, 181, 211, 223, 227, 251, 257, 269, 283, 293, 311, 317, 347, 349, 353, 359, 367, 373, 383, 389, 397, 401, 419, 439, 457, 461, 463, 479, 487, 499, 503, 509, 523, 547, 557, 587, 593, 607
CROSSREFS
See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141785 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A107152, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).
Primes of the form 3*x^2 + 5*x*y - 5*y^2 (as well as of the form 7*x^2 + 13*x*y + 3*y^2).
+10
2
3, 5, 7, 17, 23, 37, 73, 97, 107, 113, 163, 167, 173, 193, 197, 227, 233, 277, 283, 313, 317, 337, 347, 367, 397, 487, 503, 547, 607, 617, 643, 653, 673, 677, 683, 743, 787, 823, 827, 853, 857, 877, 887, 907, 947, 983, 997, 1013, 1093, 1117, 1153, 1163, 1187
CROSSREFS
Cf. A141773 (d=85). See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141785 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A107152, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).
Primes of the form 4*x^2 + 3*x*y - 5*y^2 (as well as of the form 8*x^2 + 11*x*y + y^2).
+10
1
2, 5, 11, 17, 47, 53, 67, 71, 73, 79, 89, 97, 107, 109, 131, 139, 157, 167, 173, 179, 199, 223, 227, 233, 251, 257, 263, 269, 271, 277, 283, 307, 311, 317, 331, 347, 367, 373, 401, 409, 443, 449, 461, 463, 467, 479, 487, 509, 523, 587, 601, 607, 613, 619, 631
CROSSREFS
See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141785 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A107152, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141772, A141773 (d=85). A141776, A141777 (d=88). A141778 (d=89). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).
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