A334819 -id:A334819 - cp's OEIS frontend

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

Joel Brennan, Jun 14 2022

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.

			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.

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

Cf. A088198, A334819, A088196.

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

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

A192450 Numbers k such that -1 is not a square mod k.

Original entry on oeis.org

3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 27, 28, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104, 105, 107, 108

Offset: 1

José María Grau Ribas, Jul 01 2011

nonn

Contains A002145 as a subsequence.

Numbers that are divisible by 4 or by a term of A002145. - Robert Israel, May 14 2020

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A008784, A002145, A334819.

filter:= n -> n mod 4 = 0 or member(3, numtheory:-factorset(n) mod 4):
select(filter, [$1..1000]); # Robert Israel, May 14 2020

Table[If[Reduce[x^2==-1,Modulus->n]===False,n],{n,2,200}]//Union

for(n=1, 1e3, if(!issquare(Mod(-1, n)), print1(n", "))) \\ Charles R Greathouse IV, Jul 04 2011

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

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