A249778 - OEIS

%I #16 Oct 02 2017 02:12:10

%S 2,7,3,4,11,25,9,19,16,49,17,59,67,121,81,169,43,115,64,191,293,361,

%T 289,587,269,841,863,961,1031,1369,441,1681,1867,2209,1849,2809,65,

%U 529,256,643,3481,3517,1639,1877,3721,4489,5041,5329,5591,6241,3557,6889,7921

%N 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.

%C 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.

%e a(1) = 2 because the next term is 7 and k(2,7) = 1;

%e a(2) = 7 because the next two terms are (3,4) => k(7,3) = 1 and k(7,4) = 1;

%e 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.

%o (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

%Y Cf. A247665, A249692.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 05 2014