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A325083
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Prime numbers congruent to 1, 65 or 81 modulo 112 representable by both x^2 + 14*y^2 and x^2 + 448*y^2.
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3
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449, 673, 977, 1409, 1873, 2017, 2081, 2129, 2417, 2657, 2753, 3313, 3697, 4001, 4561, 4657, 4673, 4817, 4993, 6689, 6833, 7057, 7121, 7393, 7457, 7793, 8017, 8353, 8369, 8689, 8849, 9377, 9473, 9857, 10193, 10273, 11057, 11393, 11489, 11953, 12161, 12289
(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 1, 65 or 81 modulo 112 are representable by both or neither of the quadratic forms x^2 + 14*y^2 and x^2 + 448*y^2. This sequence corresponds to those representable by both, and A325084 corresponds to those representable by neither.
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LINKS
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EXAMPLE
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Regarding 3313:
- 3313 is a prime number,
- 3313 = 29*112 + 65,
- 3313 = 53^2 + 14*6^2 = 39^2 + 448*2^2,
- hence 3313 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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