A191089 Least prime p such that the first n primes are not squares mod p.

3, 5, 43, 43, 67, 67, 163, 163, 163, 163, 163, 163, 74093, 170957, 360293, 679733, 2004917, 2004917, 51599563, 51599563, 96295483, 96295483, 146161723, 1408126003, 1728061733, 1728061733, 1728061733, 1728061733, 1728061733, 1728061733

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn

Comments

That is, the first n primes are quadratic non-residues mod p. A less restrictive form of A001992. Sequence A191088 is similar, but allows p to be composite. See A147972 for the square version.

Crossrefs

Cf. A001992, A147972, A191088.

Programs

Mathematica

Table[p = 2; While[Length[Select[Prime[Range[n]], JacobiSymbol[#, p] == -1 &]] < n, p = NextPrime[p]]; p, {n, 15}]

PARI

q=2;forprime(k=3,1e9,forprime(p=2,q,if(kronecker(p,k)>=0,next(2)));print1(k", ");q=nextprime(q+1);k--) \\ Charles R Greathouse IV, Oct 10 2011

Extensions

a(16)-a(30) from Charles R Greathouse IV, Oct 10 2011