A249782 a(1)=2; thereafter, a(n) is the smallest prime not yet used which is compatible with the condition that a(n) is a quadratic residue modulo a(k) for the next n indices k = n+1, n+2, ..., 2n.

2, 7, 3, 37, 11, 83, 107, 139, 43, 211, 193, 881, 751, 2777, 2633, 5981, 6563, 10531, 3407, 9871, 12421, 23873, 6449, 164789, 3547, 39877, 248909, 370081, 528883, 1144453, 574813, 1201153, 1428929, 2225053, 1397719

Offset

1,1

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.

Links

Table of n, a(n) for n=1..35.

Example

a(1) = 2 because the next term is 7 and L(2/7) = 1;
a(2) = 7 because the next two terms are (3,37) => L(7/3) = 1 and L(7/37) = 1;
a(3) = 3 because the next three terms are (37,11,83) => L(3/37) = 1, L(3/11) = 1 and L(3/83) = 1.

Prog

(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

Crossrefs

Cf. A249692, A249778.

Sequence in context: A117809 A052091 A090276 * A090564 A306618 A349856

Adjacent sequences: A249779 A249780 A249781 * A249783 A249784 A249785

Keyword

nonn,more

Author

Michel Lagneau, Nov 05 2014

Status

approved