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A059844
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a(n) = smallest nonzero square x^2 such that n+x^2 is prime.
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2
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1, 1, 4, 1, 36, 1, 4, 9, 4, 1, 36, 1, 4, 9, 4, 1, 36, 1, 4, 9, 16, 1, 36, 49, 4, 81, 4, 1, 144, 1, 16, 9, 4, 9, 36, 1, 4, 9, 4, 1, 576, 1, 4, 9, 16, 1, 36, 25, 4, 9, 16, 1, 36, 25, 4, 81, 4, 1, 324, 1, 36, 9, 4, 9, 36, 1, 4, 81, 4, 1, 36, 1, 16, 9, 4, 25, 36, 1, 4, 9, 16, 1, 144, 25, 4, 81
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) + n is the smallest prime of the form x^2 + n.
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EXAMPLE
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a(24) = 49 because 49 + 24 = 73 is prime and 1 + 24 = 25, 4 + 24 = 28, 9 + 24 = 33, 16 + 24 = 40, 25 + 24 = 49, and 36 + 24 = 60 are composite.
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MAPLE
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f:= proc(n) local x;
for x from 1 + (n mod 2) by 2 do
if isprime(n+x^2) then return x^2 fi;
od
end proc:
f(1):= 1:
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MATHEMATICA
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sqs[n_]:=Module[{q=1}, While[!PrimeQ[n+q], q=(Sqrt[q]+1)^2]; q]; Array[ sqs, 90] (* Harvey P. Dale, Aug 11 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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STATUS
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approved
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