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A325075
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Prime numbers congruent to 1, 16 or 22 modulo 39 representable by both x^2 + x*y + 10*y^2 and x^2 + x*y + 127*y^2.
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3
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139, 157, 367, 523, 547, 607, 991, 997, 1153, 1171, 1231, 1249, 1381, 1459, 1483, 1693, 1933, 1951, 2011, 2029, 2473, 2557, 3121, 3181, 3253, 3259, 3433, 3511, 3643, 3877, 4111, 4447, 4603, 4663, 4759, 5521, 5749, 5827, 6007, 6163, 6217, 6301, 6397, 6451, 6553
(list;
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listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Brink showed that prime numbers congruent to 1, 16 or 22 modulo 39 are representable by both or neither of the quadratic forms x^2 + x*y + 10*y^2 and x^2 + x*y + 127*y^2. This sequence corresponds to those representable by both, and A325076 corresponds to those representable by neither.
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LINKS
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EXAMPLE
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Regarding 997:
- 997 is a prime number,
- 997 = 25*39 + 22,
- 997 = 27^2 + 27*4 + 10*4^2 = 29^2 + 29*1 + 127*1^2,
- hence 997 belongs to this sequence.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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