A249797 a(1) = 2; thereafter, a(n) is the smallest prime not yet used which is compatible with the condition that a(n) is a non-quadratic residue modulo a(k) for the next n indices k = n + 1, n + 2, ..., 2n.

2, 3, 5, 7, 13, 67, 41, 71, 19, 97, 199, 263, 311, 7121, 3221, 8581, 373, 977, 331, 1723, 2161, 27409, 19079, 42967, 61441, 206051, 16649, 212777, 236527, 572651, 175897, 258521, 1010291, 1369559, 2530067

Offset: 1

Author

Michel Lagneau, Nov 06 2014

Keywords

• nonn
• more

Comments

L(a(n)/a(k)) = -1 for the next n indices k = n + 1, n + 2, ..., 2n where L(a/p) is the Legendre symbol.

Examples

			a(1) = 2 because the next term is 3 and L(2/3) = -1;
a(2) = 3 because the next two terms are (5, 7) => L(3/5) = -1 and L(3/7) = -1;
a(3) = 5 because the next three terms are (7, 13, 67) => L(5/7) = -1, L(5/13) = -1 and L(5/67) = -1.
		

Crossrefs

Cf. A249782.

Programs

PARI

m=35; v=vector(m); u=vectorsmall(10000*m); for(n=1, m, for(i=1, 10^9, if(!u[i], for(j=(n+1)\2, n-1, if(kronecker(v[j], prime(i))==1 || kronecker(v[j],prime(i))==0, next(2))); v[n]=prime(i); u[i]=1; break))); v