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A325068
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Prime numbers congruent to 1 modulo 16 representable neither by x^2 + 32*y^2 nor by x^2 + 64*y^2.
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2
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17, 97, 193, 241, 401, 433, 449, 641, 673, 769, 929, 977, 1009, 1297, 1361, 1409, 1489, 1697, 1873, 2017, 2081, 2161, 2417, 2609, 2753, 2801, 2897, 3041, 3169, 3329, 3457, 3617, 3697, 3793, 3889, 4129, 4241, 4337, 4561, 4673, 5009, 5153, 5281, 5441, 5521, 5857
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listen;
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OFFSET
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1,1
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COMMENTS
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Kaplansky showed that prime numbers congruent to 1 modulo 16 are representable by both or neither of the quadratic forms x^2 + 32*y^2 and x^2 + 64*y^2. A325067 corresponds to those representable by both, and this sequence corresponds to those representable by neither.
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LINKS
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EXAMPLE
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Regarding 17:
- 17 is a prime number,
- 17 = 16*1 + 1,
- 17 is representable neither by x^2 + 32*y^2 nor by x^2 + 64*y^2,
- hence 17 belongs to the 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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