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Search: id:A105345
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| A105345 |
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Primes p with class number h(-p) divisible by 16. |
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+0
1
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| 257, 353, 409, 521, 569, 809, 857, 953, 1129, 1153, 1201, 1217, 1249, 1657, 2113, 2137, 2153, 2273, 2377, 2521, 2617, 2633, 2657, 2729, 2833, 3209, 3217, 3761, 3769, 4481, 4993, 5569, 5801, 5897, 6217, 6329, 6449, 6529, 7177, 7193
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OFFSET
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1,1
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COMMENT
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These are a proper subset of the primes of the form x^2+32y^2 whose class numbers are divisible by 8.
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REFERENCES
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Cohn, H. Introduction to the construction of class fields, Cambridge, 1985, pp. 147-151
Leonard, Philip A. and Williams, Kenneth S. On the divisibility of the class numbers of Q(sqrt(-p)) and Q(sqrt(-2p)) by 16, Canadian Math Bulletin,v.25 (1982), pp. 200-6
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EXAMPLE
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h(-257)=16: binary quadratic forms of discriminant -4(257) are x^2+257y^2, 2x^2+2xy+129y^2, 3x^2+-2xy+86y^2, 6x^2+-2xy+43y^2,9x^2+-4xy+29y^2, 7x^2+-6xy+38y^2, 14x^2+-6xy+19y^2, 13x^2+-8xy+21y^2, 17x^2+-14xy+18y^2 for 16 forms (the +- forms count twice)
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CROSSREFS
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Sequence in context: A139653 A060879 A062382 this_sequence A060261 A158231 A070815
Adjacent sequences: A105342 A105343 A105344 this_sequence A105346 A105347 A105348
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KEYWORD
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nonn
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AUTHOR
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John L. Drost (drost(AT)marshall.edu), Apr 30 2005
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