A354974 Distance LQnR(n) (A334819) from n.

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1

Offset: 3

Author

Joel Brennan, Jun 14 2022

Keywords

• nonn
• easy

Comments

a(n) is the distance between n and the largest quadratic nonresidue modulo n: a(n) = n - A334819(n). So n - a(n) is the largest nonsquare modulo n.

Examples

			The nonsquares modulo 8 are 2, 3, 5, 6, and 7, so the distance of the largest quadratic nonresidue from 8 is a(8) = 1. The quadratic nonresidues modulo 17 are 3, 5, 6, 7, 10, 11, 12, and 14, so a(17) = 17 - 14 = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A088198, A334819, A088196.

Programs

Mathematica

a[n_] := n - Max @ Complement[Range[n - 1], Mod[Range[n/2]^2, n]]; Array[a, 100, 3] (* Amiram Eldar, Jun 15 2022 *)

PARI

a(n) = forstep(r = n - 1, 1, -1, if(!issquare(Mod(r, n)), return(n-r))) \\ Thomas Scheuerle, Jun 15 2022