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A068486
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Smallest prime equal to n^2 + m^2 with n >= m.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| With i being the imaginary unit, the numbers m + ni and m - ni are Gaussian primes. [From Alonso del Arte, Feb 07 2011]
All elements after the first are congruent to 1 (mod 4). - Carmine Suriano, Mar 30 2011
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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MAPLE
| 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
| Table[k = 1; While[p = n^2 + k^2; Not[PrimeQ[p]], k++]; p, {n, 50}] (* From Alonso del Arte, Feb 07 2011 *)
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CROSSREFS
| Cf. A068487. The values of m are given by A069003.
Sequence in context: A002313 A177349 A160215 * A099332 A031439 A074856
Adjacent sequences: A068483 A068484 A068485 * A068487 A068488 A068489
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 11 2002
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 17 2002
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