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.
%I A101685 #4 May 26 2024 02:33:45
%S A101685 1,-1,3,1,-1,3,1,-1,3,1,-2,4,1,-2,4,1,-1,3,1,-1,3,1,-3,5,1,-3,5,1,-1,
%T A101685 3,1,-1,3,1,-2,4,1,-2,4,1,-1,3,1,-1,3,1,-4,6,1,-4,6,1,-1,3,1,-1,3,1,
%U A101685 -2,4,1,-2,4,1,-1,3,1,-1,3,1,-3,5,1,-3,5,1,-1,3,1,-1,3,1,-2,4,1,-2,4
%N A101685 First differences of A101684.
%C A101685 Presumably the sequence can be derived from A007814.
%F A101685 a(n) = A101684(n+1) - A101684(n). - _Wesley Ivan Hurt_, May 26 2024
%t A101685 Differences[IntegerExponent[Denominator[With[{nn = 80}, CoefficientList[Series[Exp[-1 + Sqrt[1 + x]], {x, 0, nn}], x] Range[0, nn]!]], 2]] (* _Wesley Ivan Hurt_, May 26 2024 after _Harvey P. Dale_ *)
%Y A101685 Cf. A007814, A101684.
%K A101685 sign
%O A101685 0,3
%A A101685 _Ralf Stephan_, Dec 13 2004