cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

David W. Wilson

Keywords

Comments

Complement of A037041. - Michel Marcus, Nov 11 2015

Crossrefs

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).

Programs

  • Mathematica
    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 *)

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

Views

Author

T. D. Noe, Aug 25 2005

Keywords

Examples

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

Crossrefs

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

Programs

  • Mathematica
    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}]

A111988 Greatest number having n quadratic residues, or 0 if there is no such number.

Original entry on oeis.org

1, 4, 8, 16, 0, 24, 32, 48, 40, 19, 27, 80, 0, 96, 29, 144, 0, 120, 37, 76, 160, 108, 128, 240, 0, 0, 136, 288, 0, 152, 81, 336, 216, 67, 0, 360, 73, 148, 0, 304, 0, 480, 0, 432, 232, 384, 0, 720, 416, 0, 101, 103, 125, 440, 109, 672, 296, 0, 0, 464, 0, 324, 544, 1008, 0
Offset: 1

Views

Author

T. D. Noe, Aug 25 2005

Keywords

Examples

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

Crossrefs

Cf. A037046 (n such that a(n)=0), A111986 (number of numbers having n quadratic residues), A111987 (least number having n quadratic residues).

Programs

  • Mathematica
    t=Table[Length[Union[Mod[Range[0, n/2]^2, n]]], {n, 10000}]; Table[pos=Flatten[Position[t, n]]; If[Length[pos]==0, 0, Last[pos]], {n, 100}]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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