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

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, 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, 7, 2, 3, 2, 13, 3, 5, 5, 3, 2, 7, 2, 5, 11, 3, 0, 5, 2

Offset: 0

Author

Peter Luschny, May 26 2024

Keywords

• nonn

Crossrefs

Similar: A092419, A144294.

Cf. A372728.

Programs

Maple

K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
a := proc(n) if issqr(n) then return 0 fi;
local k; k := 0;
    while true do
        if K(n, k) = -1 then return k fi;
        k := k + 1;
od; -1; end:
seq(a(n), n = 0..83);

PARI

a(n) = if (issquare(n), 0, my(k=1); while (kronecker(n,k) != -1, k++); k); \\ Michel Marcus, May 31 2024

SageMath

def A373088(n):
    if is_square(n): return 0
    k = 0
    while True:
        if kronecker_symbol(n, k) == -1:
            return k
        k += 1
    return k
print([A373088(n) for n in range(83)])

Formula

If n is not a square then a(n) is a prime number.