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A144294
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Let k = n-th nonsquare = A000037(n); then a(n) = smallest prime p such that k is not a square mod p.
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7
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3, 5, 3, 7, 5, 3, 7, 3, 5, 5, 3, 13, 3, 5, 7, 3, 11, 5, 3, 7, 3, 5, 5, 3, 11, 7, 3, 5, 7, 3, 5, 3, 11, 7, 3, 5, 5, 3, 7, 11, 3, 5, 3, 11, 5, 3, 7, 7, 3, 5, 5, 3, 13, 7, 3, 5, 3, 7, 5, 3, 7, 13, 3, 5, 5, 3, 7, 7, 3, 5, 11, 3, 5, 3, 11, 11, 3, 5, 5, 3, 7, 17, 3, 5, 7, 3, 7, 5, 3, 13
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OFFSET
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1,1
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COMMENTS
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In a posting to the Number Theory List, Oct 15 2008, Kurt Foster remarks that a positive integer M is a square iff M is a quadratic residue mod p for every prime p which does not divide M. He then asks how fast the present sequence grows.
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LINKS
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MAPLE
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with(numtheory); f:=proc(n) local M, i, j, k; M:=100000; for i from 2 to M do if legendre(n, ithprime(i)) = -1 then RETURN(ithprime(i)); fi; od; -1; end;
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PROG
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(PARI) a(n)=my(k=n+(sqrtint(4*n)+1)\2); forprime(p=2, , if(!issquare(Mod(k, p)), return(p))) \\ Charles R Greathouse IV, Aug 28 2016
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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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