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A263979
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Least prime p of the form p = a^2 + b^2 with a > n and b > n.
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1
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2, 13, 41, 41, 61, 113, 113, 181, 181, 269, 313, 313, 421, 421, 613, 613, 613, 761, 761, 929, 1013, 1013, 1201, 1201, 1301, 1637, 1741, 1741, 1741, 1861, 2113, 2113, 2381, 2381, 2521, 2969, 2969, 3121, 3121, 3449, 3613, 3613, 4153, 4337, 4513, 4513, 4513, 5101, 5101, 5101, 5737, 5953, 6173, 6389, 6389, 6857, 7321, 7321, 7321, 7321
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OFFSET
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0,1
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COMMENTS
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a(n) exists for every n; see Sierpinski (1988), p. 221.
The distinct primes in the sequence form A263980.
Conjecture: a(n) <= 2*(2n+1)^2 for all n >= 0.
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REFERENCES
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W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988.
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LINKS
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FORMULA
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a(n) == 1 or 2 mod 4.
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EXAMPLE
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The smallest prime of the form a^2 + b^2 with a > 2 and b > 2 is 41 = 4^2 + 5^2, so a(2) = 41 and a(3) = 41.
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MATHEMATICA
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Table[ Min[ Select[ Union[ Flatten[ With[{n = k}, Array[#1^2 + #2^2 &, {2n + 1, 2n + 1}, {n + 1, n + 1}] ]]], PrimeQ]], {k, 0, 59}] (* This assumes the Conjecture above. *)
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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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