|
%I #10 Mar 07 2013 17:12:42
%S 5,13,61,109,421,1621,7309,8941,13381,82021,365509,300301,1336141,
%T 644869,8658589,3462229,6810301,16145221,165163909,43030381,163384621,
%U 249623581,2283397141,1272463669,2055693949
%N 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).
%C 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).
%t 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
%Y Cf. A096634, A096636.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Jun 24 2004
%E Better name from _Jonathan Sondow_, Mar 07 2013
|
