A249778 a(1)=2; thereafter, a(n) is the smallest number not occurring earlier such that Kronecker(a(k), a(n)) = 1 for the next n indices k = n+1, n+2, ..., 2n.

2, 7, 3, 4, 11, 25, 9, 19, 16, 49, 17, 59, 67, 121, 81, 169, 43, 115, 64, 191, 293, 361, 289, 587, 269, 841, 863, 961, 1031, 1369, 441, 1681, 1867, 2209, 1849, 2809, 65, 529, 256, 643, 3481, 3517, 1639, 1877, 3721, 4489, 5041, 5329, 5591, 6241, 3557, 6889, 7921

Offset

1,1

Comments

Kronecker(i,j) is an extension of the Jacobi symbol to all integers. The sequence with the condition Kronecker(a(i), a(n)) = -1/+1 is given by A247665.

Links

Table of n, a(n) for n=1..53.

Example

a(1) = 2 because the next term is 7 and k(2,7) = 1;
a(2) = 7 because the next two terms are (3,4) => k(7,3) = 1 and k(7,4) = 1;
a(3) = 3 because the next three terms are (4,11,25) => k(3,4)= 1, k(3,11) = 1 and k(3,25) = 1.

Prog

(PARI) m=55; v=vector(m); u=vectorsmall(1000*m); for(n=1, m, for(i=2, 10^9, if(!u[i], for(j=(n+1)\2, n-1, if(kronecker(v[j], i)==-1 || kronecker(v[j], i)==0, next(2))); v[n]= i; u[i]=1; break))); v

Crossrefs

Cf. A247665, A249692.

Sequence in context: A257102 A371707 A226626 * A350505 A326661 A326662

Adjacent sequences: A249775 A249776 A249777 * A249779 A249780 A249781

Keyword

nonn

Author

Michel Lagneau, Nov 05 2014

Status

approved