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

%I #17 Oct 15 2024 15:43:06

%S 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,

%T 53,11,57,59,61,63,13,67,69,71,73,3,77,79,81,83,17,87,89,91,93,19,97,

%U 99,101,103,21,107,109,111,113

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

%H G. C. Greubel, <a href="/A033465/b033465.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) = numerator of (2*n+1)/((n^2+1)*((n+1)^2+1)). - _G. C. Greubel_, Oct 14 2024

%t Numerator[Abs[Differences[1/(Range[0,60]^2+1)]]] (* _Harvey P. Dale_, May 01 2013 *)

%o (Magma)

%o A033465:= func< n | Numerator((2*n+1)/((n^2+1)*((n+1)^2+1))) >;

%o [A033465(n): n in [0..70]]; // _G. C. Greubel_, Oct 14 2024

%o (SageMath)

%o def A033465(n): return numerator((2*n+1)/((n^2+1)*((n+1)^2+1)))

%o [A033465(n) for n in range(71)] # _G. C. Greubel_, Oct 14 2024

%Y Cf. A033466 (denominators).

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_