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 1-2 of 2 results.

A099024 a(n) = A033466(5n+2). Values of A033466(n) that differ from A058031(n+1)+1.

Original entry on oeis.org

10, 650, 986, 18850, 51410, 114610, 223450, 79186, 653050, 1018810, 1520210, 2187250, 610586, 4153250, 5527210, 7216810, 9267050, 2345186, 14644450, 18076610, 22079410, 26712850, 6407986, 38126650, 45042010, 52858010
Offset: 0

Views

Author

Ralf Stephan, Sep 25 2004

Keywords

Crossrefs

Cf. A096431 (numerators).

Programs

  • Magma
    A099024:= func< n | Denominator((2*n+1)/((n^2+(2*n+1)^2)*((5*n+3)^2+1))) >;
    [A099024(n): n in [0..40]]; // G. C. Greubel, Oct 14 2024
    
  • Mathematica
    Table[Denominator[(2*n+1)/((n^2+(2*n+1)^2)*(1+(5*n+3)^2))], {n,0,40}] (* G. C. Greubel, Oct 14 2024 *)
  • SageMath
    def A099024(n): return denominator((2*n+1)/((n^2+(2*n+1)^2)*((5*n+3)^2+1)))
    [A099024(n) for n in range(41)] # G. C. Greubel, Oct 14 2024

Formula

G.f.: P(x)/(1-x^5)^5, where P(x) is a 24-degree polynomial.
a(n) = denominators of (2*n+1)/((n^2+(2*n+1)^2)*(1+(5*n+3)^2)). - G. C. Greubel, Oct 14 2024

A033465 Numerators of the first differences of 1/(n^2 + 1).

Original entry on oeis.org

1, 3, 1, 7, 9, 11, 13, 3, 17, 19, 21, 23, 1, 27, 29, 31, 33, 7, 37, 39, 41, 43, 9, 47, 49, 51, 53, 11, 57, 59, 61, 63, 13, 67, 69, 71, 73, 3, 77, 79, 81, 83, 17, 87, 89, 91, 93, 19, 97, 99, 101, 103, 21, 107, 109, 111, 113
Offset: 0

Views

Author

Keywords

Crossrefs

Cf. A033466 (denominators).

Programs

  • Magma
    A033465:= func< n | Numerator((2*n+1)/((n^2+1)*((n+1)^2+1))) >;
    [A033465(n): n in [0..70]]; // G. C. Greubel, Oct 14 2024
    
  • Mathematica
    Numerator[Abs[Differences[1/(Range[0,60]^2+1)]]] (* Harvey P. Dale, May 01 2013 *)
  • SageMath
    def A033465(n): return numerator((2*n+1)/((n^2+1)*((n+1)^2+1)))
    [A033465(n) for n in range(71)] # G. C. Greubel, Oct 14 2024

Formula

a(n) = numerator of (2*n+1)/((n^2+1)*((n+1)^2+1)). - G. C. Greubel, Oct 14 2024
Showing 1-2 of 2 results.