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A325082
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Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 69*y^2.
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3
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89, 179, 419, 449, 599, 619, 709, 719, 829, 859, 1039, 1109, 1259, 1489, 1549, 1709, 1879, 2039, 2099, 2179, 2539, 2579, 2689, 2909, 3169, 3259, 3359, 3389, 3499, 3919, 4019, 4159, 4229, 4349, 4409, 4799, 4909, 5009, 5039, 5179, 5449, 5569, 5659, 5779, 5839
(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. A325081 corresponds to those representable by the first form, and this sequence corresponds to those representable by the second form.
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LINKS
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EXAMPLE
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Regarding 2099:
- 2099 is a prime number,
- 2099 = 38*55 + 9,
- 2099 = 17^2 + 1*17*5 + 69*5^2,
- hence 2099 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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