A373180 - OEIS

A373180

a(n) = min{k : KroneckerSymbol(n, k) = 1} if n > 1 and k > 1, a(0) = 1, a(1) = 0.

1, 0, 7, 4, 3, 4, 5, 2, 7, 2, 3, 4, 11, 3, 5, 2, 3, 2, 7, 3, 9, 4, 3, 2, 5, 2, 5, 4, 3, 4, 7, 2, 7, 2, 3, 4, 5, 3, 9, 2, 3, 2, 11, 3, 5, 4, 3, 2, 11, 2, 7, 4, 3, 4, 5, 2, 5, 2, 3, 4, 7, 3, 9, 2, 3, 2, 5, 3, 9, 4, 3, 2, 7, 2, 5, 4, 3, 4, 7, 2, 9, 2, 3, 4, 5, 3, 5

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OFFSET

0,3

COMMENTS

The Kronecker symbol only takes the values -1, 0, and 1. One can ask about the first appearance of these values in the rows of the square array K(n, k) with n, k >= 2, and supplement for boundary values n, k = 0, 1. Answers can be found in A373088 (case -1), A020639 (case 0), and in this sequence (case 1).

LINKS

Table of n, a(n) for n=0..86.

MAPLE

K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):

a := proc(n) if n < 2 then return 1 - n fi;

local k; k := 2;

while true do

if K(n, k) = 1 then return k fi;

k := k + 1;

od; -1; end:

seq(a(n), n = 0..86);

PROG

(SageMath)

def A373180(n):

if n < 2: return 1 - n

k = 2

while True:

if kronecker_symbol(n, k) == 1:

return k

k += 1

return -1

print([A373180(n) for n in range(87)])

(PARI) a(n) = if (n < 2, 1 - n, my(k=2); while(kronecker(n, k)!=1, k++); k); \\ Michel Marcus, May 27 2024

CROSSREFS

Cf. A372728, A373088, A020639.

Sequence in context: A296474 A194705 A344906 * A243309 A244817 A303612

Adjacent sequences: A373177 A373178 A373179 * A373181 A373182 A373183

KEYWORD

nonn

AUTHOR

Peter Luschny, May 27 2024

STATUS

approved