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Smallest prime p > prime(n+2) such that the first n odd primes 3, 5, 7, 11, ..., prime(n+1) are quadratic residues mod p, and prime(n+2) is a quadratic non-residue mod p.
2

%I #7 Mar 06 2013 22:14:21

%S 5,13,11,59,421,131,1811,2939,13381,12011,66491,148139,275651,644869,

%T 2269739,3462229,6810301,16145221,120078131

%N Smallest prime p > prime(n+2) such that the first n odd primes 3, 5, 7, 11, ..., prime(n+1) are quadratic residues mod p, and prime(n+2) is a quadratic non-residue mod p.

%C Same as smallest prime p such that the Legendre symbol (q|p) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (q|p) = -1 for q = prime(n+2).

%t f[n_] := Block[{k = 2}, While[JacobiSymbol[Prime[k], n] == 1, k++]; Prime[k]]; nn = 15; t = Table[0, {nn}]; t[[1]] = 1; n = 2; While[Min[t] == 0, n++; p = Prime[n]; a = f[p]; ppa = PrimePi[a]; If[ppa <= nn && t[[ppa]] == 0, t[[ppa]] = p]]; Rest[t]

%Y Cf. A096636 (p and q switched).

%K nonn

%O 0,1

%A _T. D. Noe_, Mar 06 2013

%E Simpler definition from _Jonathan Sondow_, Mar 06 2013