A096639 Smallest prime p == 5 mod 8 (A007521) 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).

5, 13, 61, 109, 421, 1621, 7309, 8941, 13381, 82021, 365509, 300301, 1336141, 644869, 8658589, 3462229, 6810301, 16145221, 165163909, 43030381, 163384621, 249623581, 2283397141, 1272463669, 2055693949

Offset: 0

Author

Robert G. Wilson v, Jun 24 2004

Keywords

• nonn

Comments

Same as smallest prime p == 5 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).

Crossrefs

Cf. A096634, A096636.

Programs

Mathematica

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] == 5, a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]]], {n, 10^9}]; t

Extensions

Better name from Jonathan Sondow, Mar 07 2013