A111988 -id:A111988 - cp's OEIS frontend

A037046 Numbers that are not the number of quadratic residues mod n for any n.

5, 13, 17, 25, 26, 29, 35, 39, 41, 43, 47, 50, 58, 59, 61, 65, 67, 71, 73, 78, 83, 85, 86, 89, 94, 95, 101, 103, 107, 109, 113, 116, 118, 119, 122, 123, 125, 127, 130, 131, 134, 143, 145, 146, 149, 155, 163, 167, 170, 173, 178, 179, 181, 183, 185, 188, 191, 193

Offset: 1

David W. Wilson

nonn

Complement of A037041. - Michel Marcus, Nov 11 2015

Cf. A000224, A096008, A111986 (number of numbers having n quadratic residues), A111987 (least number having n quadratic residues), A111988 (greatest number having n quadratic residues).

s = Length[Union@ #] & /@ Table[Mod[k^2, n], {n, 10000}, {k, 0, n - 1}]; Complement[Range@ Max@ #, #] &@ Take[Union@ s, 136] (* Michael De Vlieger, Nov 10 2015 *)

A111986 Number of numbers having n quadratic residues.

Original entry on oeis.org

1, 3, 2, 5, 0, 5, 2, 6, 2, 1, 2, 12, 0, 4, 1, 6, 0, 6, 1, 3, 4, 7, 1, 17, 0, 0, 3, 7, 0, 6, 2, 6, 3, 1, 0, 15, 1, 3, 0, 6, 0, 11, 0, 14, 3, 1, 0, 24, 2, 0, 1, 1, 1, 10, 1, 8, 3, 0, 0, 13, 0, 5, 5, 7, 0, 10, 0, 3, 2, 3, 0, 26, 0, 3, 1, 6, 4, 0, 2, 9, 3, 1, 0, 25, 0, 0, 2, 18, 0, 13, 1, 3, 4, 0, 0, 26

Offset: 1

T. D. Noe, Aug 25 2005

nonn

			a(4)=5 because the numbers 6, 7, 9, 12 and 16 each have 4 quadratic residues.

Cf. A037041 (n such that a(n)>0), A037046 (n such that a(n)=0), A111987 (least number having n quadratic residues), A111988 (greatest number having n quadratic residues).

t=Table[Length[Union[Mod[Range[0, n/2]^2, n]]], {n, 10000}]; Table[Length[Position[t, n]], {n, 100}]

A111987 Least number having n quadratic residues, or 0 if there is no number.

Original entry on oeis.org

1, 2, 5, 6, 0, 10, 13, 14, 17, 19, 25, 22, 0, 26, 29, 31, 0, 34, 37, 38, 41, 43, 128, 46, 0, 0, 53, 78, 0, 58, 61, 62, 135, 67, 0, 71, 73, 74, 0, 79, 0, 82, 0, 86, 89, 384, 0, 94, 97, 0, 101, 103, 125, 106, 109, 121, 113, 0, 0, 118, 0, 122, 205, 127, 0, 131, 0, 134, 137, 139, 0

Offset: 1

T. D. Noe, Aug 25 2005

nonn

			a(4)=6 because, of the five numbers having 4 quadratic residues (6,7,9,12,16), the least is 6.

Cf. A037046 (n such that a(n)=0), A111986 (number of numbers having n quadratic residues), A111988 (greatest number having n quadratic residues).

t=Table[Length[Union[Mod[Range[0, n/2]^2, n]]], {n, 10000}]; Table[pos=Flatten[Position[t, n]]; If[Length[pos]==0, 0, First[pos]], {n, 100}]

cp's OEIS Frontend

A037046 Numbers that are not the number of quadratic residues mod n for any n.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A111986 Number of numbers having n quadratic residues.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A111987 Least number having n quadratic residues, or 0 if there is no number.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica