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A068486
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Smallest prime equal to n^2 + m^2 with n >= m.
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3
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2, 5, 13, 17, 29, 37, 53, 73, 97, 101, 137, 193, 173, 197, 229, 257, 293, 349, 397, 401, 457, 509, 593, 577, 641, 677, 733, 809, 857, 1021, 977, 1033, 1093, 1181, 1229, 1297, 1373, 1453, 1621, 1601, 1697, 1789, 1913, 2017, 2029, 2141, 2213, 2473, 2417, 2549
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OFFSET
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1,1
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COMMENTS
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With i being the imaginary unit, the numbers m + ni and m - ni are Gaussian primes. - Alonso del Arte, Feb 07 2011
All terms after the first are congruent to 1 (mod 4). - Carmine Suriano, Mar 30 2011
Any value can occur at most once (a consequence of Alonso del Arte's comment plus unique factorization in the Gaussian integers). - Robert Israel, Aug 19 2014
Smallest prime of the form (x^2 + y^2)/2 such that |x| + |y| = 2n. Note: |x| = n - m and |y| = n + m. - Thomas Ordowski and Altug Alkan, Jan 13 2017
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LINKS
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FORMULA
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MAPLE
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for n from 1 to 100 do m := 1:while(not isprime(n^2+m^2)) do m := m+1; end do:a[n] := n^2+m^2:end do:q := seq(a[i], i=1..100);
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MATHEMATICA
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Table[k = 1; While[p = n^2 + k^2; Not[PrimeQ[p]], k++]; p, {n, 50}] (* Alonso del Arte, Feb 07 2011 *)
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PROG
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(PARI) a(n) = for (m=1, n, if (isprime(p=n^2+m^2), return (p))); \\ Michel Marcus, Jan 22 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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