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A325087
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Prime numbers congruent to 1 or 169 modulo 240 representable by both x^2 + 150*y^2 and x^2 + 960*y^2.
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3
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1129, 3361, 3769, 4801, 5209, 5449, 5521, 5689, 8329, 8641, 9601, 9769, 10009, 10321, 10729, 12409, 13681, 15121, 15289, 15361, 15601, 16561, 16729, 17041, 17209, 17761, 18169, 18481, 20089, 21529, 21601, 23761, 24001, 24169, 25609, 25849, 26641, 26881, 27529
(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 or 169 modulo 240 are representable by both or neither of the quadratic forms x^2 + 150*y^2 and x^2 + 960*y^2. This sequence corresponds to those representable by both, and A325088 corresponds to those representable by neither.
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LINKS
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EXAMPLE
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Regarding 10009:
- 10009 is a prime number,
- 10009 = 41*240 + 169,
- 10009 = 97^2 + 0*97*2 + 150*2^2 = 37^2 + 960*3^2,
- hence 10009 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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