A367034 a(n) is the smallest odd number k > 1 for which the Jacobi symbol (n / k) >= 0.

3, 3, 7, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5

Offset: 0

Author

Amiram Eldar and Thomas Ordowski, Nov 02 2023

Keywords

• nonn
• easy

Comments

This sequence is periodic with period P = 3*5*7 = 105.

All terms are in {3, 5, 7, 9}.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11025

Crossrefs

Cf. A366973.

Programs

Mathematica

a[n_] := Module[{k = 3}, While[JacobiSymbol[n, k] < 0, k += 2]; k]; Array[a, 105, 0]

PARI

a(n) = my(k=3); while(kronecker(n,k)<0, k+=2); k; \\ Michel Marcus, Nov 02 2023

Formula

a(n + 105) = a(n).