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A325081
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Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 14*y^2.
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3
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59, 199, 229, 269, 379, 389, 499, 509, 839, 929, 1049, 1279, 1409, 1439, 1499, 1609, 1699, 2029, 2069, 2269, 2399, 2699, 2729, 2819, 3019, 3089, 3469, 3529, 3719, 4049, 4079, 4129, 4139, 4339, 4519, 4679, 4789, 4889, 4999, 5119, 5399, 5479, 5669, 6029, 6229
(list;
graph;
refs;
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 4, 9, 14, 34 or 49 modulo 55 are representable by exactly one of the quadratic forms x^2 + x*y + 14*y^2 or x^2 + x*y + 69*y^2. This sequence corresponds to those representable by the first form, and A325082 corresponds to those representable by the second form.
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LINKS
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EXAMPLE
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Regarding 4999:
- 4999 is a prime number,
- 4999 = 90*55 + 49,
- 4999 = 41^2 + 41*14 + 14*14^2,
- hence 4999 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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