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.

A028736 Nonsquares mod 23.

Original entry on oeis.org

5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			Since 11 is not a perfect square and there are no solutions to x^2 = 11 mod 23, 11 is in the sequence.
Although 12 is not a perfect square either, there are solutions to x^2 = 12 mod 23, such as x = 9, x = 14. Thus 12 is not in the sequence.

References

  • Srinivasa Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962. See "Congruence properties of partitions", p. 230. - N. J. A. Sloane, Jun 01 2014

Links

Crossrefs

Cf. A010385, A028759, A278579.

Programs

  • Mathematica
    Select[Range[22], JacobiSymbol[#, 23] != 1 &] (* Jean-François Alcover, Oct 07 2018 *)
  • Scala
    val squaresMod23 = (0 to 22).map(n => n * n).map(_ % 23)
(0 to 22).diff(squaresMod23) // Alonso del Arte, Nov 23 2019

A278579 Quadratic non-residues of 23: numbers n such that Jacobi(n,23) = -1.

Original entry on oeis.org

5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22, 28, 30, 33, 34, 37, 38, 40, 42, 43, 44, 45, 51, 53, 56, 57, 60, 61, 63, 65, 66, 67, 68, 74, 76, 79, 80, 83, 84, 86, 88, 89, 90, 91, 97, 99, 102, 103, 106, 107, 109, 111, 112, 113, 114, 120, 122, 125, 126, 129, 130, 132, 134, 135, 136, 137, 143, 145, 148, 149
Offset: 1

Views

Author

N. J. A. Sloane, Nov 29 2016

Keywords

Comments

Important for the study of Ramanujan numbers A000594.

References

  • Wilton, John Raymond. "Congruence properties of Ramanujan's function τ(n)." Proceedings of the London Mathematical Society 2.1 (1930): 1-10. See page 1.

Links

Crossrefs

Cf. A028736, A000594, A063987, A278580, A028759 (=first 22 terms).
For the primes in this sequence see A191065.

Programs

  • Mathematica
    LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,1,-1},{5,7,10,11,14,15,17,19,20,21,22,28},80] (* Harvey P. Dale, Jan 12 2020 *)

Formula

From Robert Israel, Nov 30 2016: (Start)
a(n+11) = a(n)+23.
G.f.: (x^11+x^10+x^9+x^8+2*x^7+2*x^6+x^5+3*x^4+x^3+3*x^2+2*x+5)/(x^12-x^11-x+1). (End)

A010407 Squares mod 46.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 23, 24, 25, 26, 27, 29, 31, 32, 35, 36, 39, 41
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A028759.

Programs

  • Mathematica
    Union[PowerMod[Range[46], 2, 46]] (* Alonso del Arte, Dec 23 2019 *)
  • Sage
    [quadratic_residues(46)] # Zerinvary Lajos, May 24 2009
  • Scala
    (1 to 46).map(n => (n * n) % 46).toSet.toSeq.sorted // Alonso del Arte, Dec 23 2019
Showing 1-3 of 3 results.

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

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