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A376999 a(n) is the least number k that is a quadratic residue modulo prime(n) but is a quadratic nonresidue modulo all previous odd primes.

%I A376999 #18 Oct 20 2024 13:45:21
%S A376999 0,5,2,38,17,83,362,167,227,2273,398,5297,64382,69467,116387,238262,
%T A376999 214037,430022,5472953,9481097,8062073,41941577,86374763,312521282
%N A376999 a(n) is the least number k that is a quadratic residue modulo prime(n) but is a quadratic nonresidue modulo all previous odd primes.
%e A376999 a(5) = 38 because 38 is a quadratic residue modulo prime(5) = 11 but is not a quadratic residue modulo the previous odd primes 3, 5 and 7, and no number smaller than 38 works.
%p A376999 f:= proc(n) local k,p;
%p A376999   p:= 2;
%p A376999   for k from 2 do
%p A376999       p:= nextprime(p);
%p A376999       if numtheory:-quadres(n,p) = 1 then return k fi
%p A376999   od
%p A376999 end proc:
%p A376999 V:= Array(2..25): count:= 0:
%p A376999 for k from 2 while count < 24 do
%p A376999   v:= f(k);
%p A376999 if v > 0 and v <= 25 and V[v] = 0 then
%p A376999   V[v]:= k; count:= count+1;
%p A376999 fi;
%p A376999 od:
%p A376999 V[2]:= 0:
%p A376999 convert(V,list);
%Y A376999 Cf. A377212.
%K A376999 nonn
%O A376999 2,2
%A A376999 _Robert Israel_, Oct 20 2024