A222756 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.

5, 13, 11, 59, 421, 131, 1811, 2939, 13381, 12011, 66491, 148139, 275651, 644869, 2269739, 3462229, 6810301, 16145221, 120078131

Offset: 0

Author

T. D. Noe, Mar 06 2013

Keywords

• nonn

Comments

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).

Crossrefs

Cf. A096636 (p and q switched).

Programs

Mathematica

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]

Extensions

Simpler definition from Jonathan Sondow, Mar 06 2013