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A377380 a(n) is the first positive number k such that k is alternately a quadratic residue and nonresidue modulo the first n primes, but not the n+1'th.

%I A377380 #11 Oct 27 2024 10:46:30
%S A377380 1,2,11,41,26,5,671,89,59,1181,1991,3755,21521,34145,25994,137885,
%T A377380 61106,1503029,2617439,1008551,2897081,22363295,33603926,36518450,
%U A377380 79865294,185914490,593068985,2211452939,2120224529,1673286179,2644173521,1976870465
%N A377380 a(n) is the first positive number k such that k is alternately a quadratic residue and nonresidue modulo the first n primes, but not the n+1'th.
%C A377380 a(n) == 2 (mod 3) for n >= 2.
%e A377380 a(3) = 11 because 11 is a quadratic residue mod 2, a nonresidue mod 3, a residue mod 5, but a residue mod 7, and no smaller number works.
%p A377380 with(numtheory):
%p A377380 N:= 20:
%p A377380 V:= Vector(N): V[1]:= 1: count:= 1:
%p A377380 for x from 2 by 3 while count < N do
%p A377380   p:= 1:
%p A377380   for m from 0 do
%p A377380     p:= nextprime(p);
%p A377380     if numtheory:-quadres(x,p) <> (-1)^m then break fi;
%p A377380   od;
%p A377380   if V[m] = 0 then
%p A377380     V[m]:= x; count:= count+1;
%p A377380   fi
%p A377380 od:
%p A377380 convert(V,list);
%Y A377380 Cf. A096636, A377212.
%K A377380 nonn
%O A377380 1,2
%A A377380 _Robert Israel_, Oct 27 2024