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 A113778 #22 Mar 23 2024 12:20:16
%S A113778 4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13,20,19,18,17,24,23,22,21,28,27,
%T A113778 26,25,32,31,30,29,36,35,34,33,40,39,38,37,44,43,42,41,48,47,46,45,52,
%U A113778 51,50,49,56,55,54,53,60,59,58,57,64,63,62,61,68,67,66
%N A113778 Invert blocks of four in the sequence of natural numbers.
%H A113778 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A113778 a(n) = k*floor((n+k-1)/k)-(n-1) mod k; k=4, n=1, 2, ...
%F A113778 a(n) = n-cos(n*pi)-2*sqrt(2)*cos((2*n+1)*pi/4). - _Jaume Oliver Lafont_, Dec 10 2008
%F A113778 G.f.: x*( 4-x-x^2-x^3+3*x^4 ) / ( (1+x)*(1+x^2)*(1-x)^2 ). - _R. J. Mathar_, Apr 02 2011
%t A113778 With[{k=4}, Table[k Floor[(n+k-1)/k]-Mod[n-1, k], {n, 1, 10k}]]
%t A113778 Reverse/@Partition[Range[100],4]//Flatten (* or *) LinearRecurrence[ {1,0,0,1,-1},{4,3,2,1,8},100] (* _Harvey P. Dale_, Mar 02 2020 *)
%Y A113778 Cf. A113655.
%K A113778 nonn,easy
%O A113778 1,1
%A A113778 _Zak Seidov_, Jan 20 2006
%E A113778 More terms from _Harvey P. Dale_, Mar 02 2020