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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.

%I A249778 #16 Oct 02 2017 02:12:10
%S A249778 2,7,3,4,11,25,9,19,16,49,17,59,67,121,81,169,43,115,64,191,293,361,
%T A249778 289,587,269,841,863,961,1031,1369,441,1681,1867,2209,1849,2809,65,
%U A249778 529,256,643,3481,3517,1639,1877,3721,4489,5041,5329,5591,6241,3557,6889,7921
%N 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.
%C A249778 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 A249778 a(1) = 2 because the next term is 7 and k(2,7) = 1;
%e A249778 a(2) = 7 because the next two terms are (3,4) => k(7,3) = 1 and k(7,4) = 1;
%e A249778 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 A249778 (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 A249778 Cf. A247665, A249692.
%K A249778 nonn
%O A249778 1,1
%A A249778 _Michel Lagneau_, Nov 05 2014