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A373088 a(n) = min{k : KroneckerSymbol(n, k) = -1} if n is not a square, 0 otherwise.

%I A373088 #9 May 31 2024 14:24:26
%S A373088 0,0,3,2,0,2,7,5,3,0,7,2,5,2,3,13,0,3,5,2,3,2,5,3,7,0,3,2,5,2,11,7,3,
%T A373088 5,7,2,0,2,3,11,7,3,5,2,3,2,11,3,5,0,3,2,5,2,7,7,3,5,5,2,13,2,3,5,0,3,
%U A373088 7,2,3,2,13,3,5,5,3,2,7,2,5,11,3,0,5,2
%N A373088 a(n) = min{k : KroneckerSymbol(n, k) = -1} if n is not a square, 0 otherwise.
%F A373088 If n is not a square then a(n) is a prime number.
%p A373088 K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
%p A373088 a := proc(n) if issqr(n) then return 0 fi;
%p A373088 local k; k := 0;
%p A373088     while true do
%p A373088         if K(n, k) = -1 then return k fi;
%p A373088         k := k + 1;
%p A373088 od; -1; end:
%p A373088 seq(a(n), n = 0..83);
%o A373088 (SageMath)
%o A373088 def A373088(n):
%o A373088     if is_square(n): return 0
%o A373088     k = 0
%o A373088     while True:
%o A373088         if kronecker_symbol(n, k) == -1:
%o A373088             return k
%o A373088         k += 1
%o A373088     return k
%o A373088 print([A373088(n) for n in range(83)])
%o A373088 (PARI) a(n) = if (issquare(n), 0, my(k=1); while (kronecker(n,k) != -1, k++); k); \\ _Michel Marcus_, May 31 2024
%Y A373088 Similar: A092419, A144294.
%Y A373088 Cf. A372728.
%K A373088 nonn
%O A373088 0,3
%A A373088 _Peter Luschny_, May 26 2024