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

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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000

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