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A106904
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Primes of the form x^2-xy+13y^2, with x and y nonnegative.
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5
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13, 19, 43, 67, 103, 127, 151, 157, 223, 229, 271, 307, 331, 349, 373, 409, 421, 433, 457, 463, 523, 577, 613, 631, 661, 727, 733, 739, 757, 769, 829, 859, 883, 919, 937, 967, 1021, 1033, 1039, 1063, 1069, 1087, 1123, 1171, 1237, 1249, 1279, 1291, 1327
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OFFSET
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1,1
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COMMENTS
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Discriminant=-51.
Also: Primes which are squares (mod 51). Differs from the subsequence A106903 (because x^2+xy+y^2 = (x+y)^2 - (x+y)y + y^2) from a(20) = 463 on, A106903(20) = 523. Terms which are not in A106903 are: 463, 631, 1033, 1039, 1279, 1291,... Up to 1279 these are also in A139643. Cf. also A191034. - M. F. Hasler, Jan 15 2016
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LINKS
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MATHEMATICA
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QuadPrimes2[1, -1, 13, 10000] (* see A106856 *)
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PROG
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(PARI) select(p->issquare(Mod(p, 51))&&isprime(p), [1..1500]) \\ See A106903 for alternative code. - M. F. Hasler, Jan 15 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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