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A096638
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Smallest prime p == 3 mod 8 (A007520) and p > prime(n+2) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1), and p is a quadratic non-residue mod prime(n+2).
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2
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11, 43, 19, 211, 331, 2011, 1171, 7459, 10651, 18379, 90931, 257371, 399499, 1234531, 6938779, 3574411, 14669251, 39803611, 102808099, 288710899, 322503091, 465390979, 1582819291, 2410622971, 505313251
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OFFSET
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0,1
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COMMENTS
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Same as smallest prime p == 3 mod 8 with the property that the Legendre symbol (p|q) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (p|q) = -1 for q = prime(n+2).
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LINKS
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MATHEMATICA
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f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; t = Table[0, {50}]; Do[p = Prime[n]; If[Mod[p, 8] == 3, a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]]], {n, 10^9}]; t
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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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