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Search: id:A087856
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| A087856 |
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Primes of the form 16m^2+25, m=1,3,5, ... |
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+0
1
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| 41, 809, 1321, 2729, 4649, 5801, 11689, 15401, 17449, 21929, 26921, 41641, 52009, 55721, 59561, 71849, 80681, 94889, 99881, 126761, 156841, 169769, 190121, 197161, 204329, 226601, 234281, 266281, 327209, 345769, 394409, 457001, 467881, 524201
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is a special case of the theorem that all prime numbers of the form 4k+1 can be expressed as the sum of two squares. Let p = a^2+b^2 then a=4n+1 and b = 4m. From this it follows that p = 16(m^2+n^2) + 8n +1. When n=1 we have p=16m^2 + 25. If we let k=16m then the arithmetic progression km + 25 has an infinite number of primes from Dirichlet's theorem.
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REFERENCES
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H. Rademacher, Lectures on Elementary Number Theory, 1964, pp. 121-136
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PROGRAM
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(PARI) fourmp1(m, n) = { forstep(x=1, m, 2, y=16*(x^2+n^2)+8*n+1; if(isprime(y), print1(y", ")) ) }
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CROSSREFS
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Cf. A087857, A087861, A087862.
Sequence in context: A060563 A167737 A125551 this_sequence A010957 A010993 A090836
Adjacent sequences: A087853 A087854 A087855 this_sequence A087857 A087858 A087859
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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 09 2003
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