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Search: id:A087877
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| A087877 |
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Primes of the form (4n+1)^2 + (4m)^2, m,n = 0,1,2.. |
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| 17, 41, 89, 97, 233, 257, 281, 313, 337, 353, 401, 433, 457, 569, 577, 601, 641, 769, 809, 857, 881, 953, 1049, 1097, 1153, 1193, 1201, 1297, 1321, 1409, 1433, 1489, 1601, 1697, 1873, 1889, 2017, 2081, 2089, 2113, 2137, 2153, 2281, 2377, 2393, 2417, 2441
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OFFSET
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1,1
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COMMENT
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If an odd number is of the form a^2 + b^2, then a and b must be one of the following forms.
a=4n+1, b=4m so that a^2+b^2 = 16(m^2+n^2) + 8n + 1 of form 4k1+1
a=4n+3, b=4m a^2+b^2 = 16(m^2+n^2) + 24n + 1 of form 4k2+1
a=4n+1, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(n+2m ) + 5 of form 4k3+1
a=4n+3, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(3n+2m) + 13 of form 4k4+1
The sequences built using these 4 forms produce all prime numbers of the form 4k+1.This particular sequence is a=4n+1, b=4m.
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CROSSREFS
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Sequence in context: A028886 A110226 A054819 this_sequence A107181 A139879 A070179
Adjacent sequences: A087874 A087875 A087876 this_sequence A087878 A087879 A087880
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 11 2003
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