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 A156351 #17 Dec 08 2021 11:31:53
%S A156351 1,1,2,2,3,4,5,5,6,7,7,8,8,9,10,10,11,11,12,13,14,14,15,16,17,17,18,
%T A156351 18,19,20,20,21,22,23,23,24,25,25,26,26,27,28,29,29,30,31,32,32,33,34,
%U A156351 34,35,35,36,37,37,38,38,39,40,41,41,42,43,43,44,44,45,46,46,47,48,49,49
%N A156351 a(n) = Sum_{k=1..n} (-1)^K(k+1)*(K(k+1)-K(k)) where K(k) = A000002(k).
%C A156351 a(n)=1 plus the number of symbol changes in the first n terms of A078880. - Jean-Marc Fedou and _Gabriele Fici_, Mar 18 2010
%H A156351 Jon Maiga, <a href="/A156351/b156351.txt">Table of n, a(n) for n = 1..10000</a>
%H A156351 J.M. Fedou and G. Fici, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL13/Fici/fici.html">Some remarks on differentiable sequences and recursivity</a>, Journal of Integer Sequences 13(3): Article 10.3.2 (2010). [From Jean-Marc Fedou and _Gabriele Fici_, Mar 18 2010]
%F A156351 n - A054353(a(n)) = 1 if n is in A078649, n - A054353(a(n)) = 0 otherwise. A078649(n + 1 - a(n)) - n takes values among {0,1,2,3}.
%F A156351 a(n) = gcd(a(a(n-1)),2) + a(n-2) (conjectured). - _Jon Maiga_, Dec 07 2021
%t A156351 a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1 + Mod[n - 1, 2]}], {n, 3, 80}, {i, 1, a2[[n]]}]; a[n_] := Sum[(-1)^a2[[k + 1]]*(a2[[k + 1]] - a2[[k]]), {k, 1, n}]; Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Jun 18 2013 *)
%Y A156351 Partial sums of A156728.
%K A156351 nonn
%O A156351 1,3
%A A156351 _Benoit Cloitre_, Feb 08 2009