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A201719
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Primes of the form x^2 + 2y^2 such that y^2 + 2x^2 is also prime.
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1
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11, 19, 43, 59, 67, 83, 107, 139, 163, 179, 211, 251, 307, 331, 419, 443, 467, 491, 563, 571, 587, 619, 643, 811, 883, 907, 947, 971, 1019, 1091, 1123, 1171, 1259, 1291, 1307, 1427, 1531, 1571, 1579, 1667, 1699, 1747, 1787, 1811, 1907, 1979, 1987, 2003, 2011
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OFFSET
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1,1
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COMMENTS
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All terms == 3 mod 8 (cf. A007520).
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LINKS
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EXAMPLE
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Corresponding pairs of primes:
(a(1),a(2))=(11,19): 11=3^2+2*1^2, 19=1^2+2*3^2
(a(3),a(4))=(43,59): 43=5^2+2*3^2, 59=3^2+2*5^2
(a(5),a(7))=(67,107): 67=7^2+2*3^2, 107=3^2+2*7^2.
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MATHEMATICA
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With[{nn=50}, Take[Union[Flatten[Select[{#[[1]]^2+2#[[2]]^2, 2#[[1]]^2+ #[[2]]^2}&/@Subsets[Range[nn], {2}], And@@PrimeQ[#]&]]], nn]] (* Harvey P. Dale, Sep 15 2013 *)
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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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