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

%I A033465 #17 Oct 15 2024 15:43:06
%S A033465 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 A033465 53,11,57,59,61,63,13,67,69,71,73,3,77,79,81,83,17,87,89,91,93,19,97,
%U A033465 99,101,103,21,107,109,111,113
%N A033465 Numerators of the first differences of 1/(n^2 + 1).
%H A033465 G. C. Greubel, <a href="/A033465/b033465.txt">Table of n, a(n) for n = 0..2000</a>
%F A033465 a(n) = numerator of (2*n+1)/((n^2+1)*((n+1)^2+1)). - _G. C. Greubel_, Oct 14 2024
%t A033465 Numerator[Abs[Differences[1/(Range[0,60]^2+1)]]] (* _Harvey P. Dale_, May 01 2013 *)
%o A033465 (Magma)
%o A033465 A033465:= func< n | Numerator((2*n+1)/((n^2+1)*((n+1)^2+1))) >;
%o A033465 [A033465(n): n in [0..70]]; // _G. C. Greubel_, Oct 14 2024
%o A033465 (SageMath)
%o A033465 def A033465(n): return numerator((2*n+1)/((n^2+1)*((n+1)^2+1)))
%o A033465 [A033465(n) for n in range(71)] # _G. C. Greubel_, Oct 14 2024
%Y A033465 Cf. A033466 (denominators).
%K A033465 nonn,frac
%O A033465 0,2
%A A033465 _N. J. A. Sloane_