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 A113605 #15 Sep 03 2017 03:28:08
%S A113605 1,1,1,2,2,3,3,5,4,4,9,5,5,14,6,7,15,7,8,16,15,9,19,16,10,21,17,11,22,
%T A113605 28,13,23,29,14,24,31,15,25,36,16,29,37,17,30,38,19,49,39,20,50,49,21,
%U A113605 57,52,22,59,53,23,60,54,29,61,55,30,66,61,31,67,62,32,69,63,35,76,64
%N A113605 a(1) = a(2) = a(3) = 1; a(n) = a(n-3) + gcd(a(n-1), a(n-2)).
%H A113605 Harvey P. Dale, <a href="/A113605/b113605.txt">Table of n, a(n) for n = 1..1000</a>
%e A113605 a(16) = a(13) + gcd(a(15), a(14)) = 5 + gcd(6,14) = 7.
%p A113605 a[1]:=1: a[2]:=1: a[3]:=1: for n from 4 to 100 do a[n]:=a[n-3]+gcd(a[n-1],a[n-2]) od: seq(a[n],n=1..90); # _Emeric Deutsch_, Feb 01 2006
%t A113605 a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 3] + GCD[a[n - 1], a[n - 2]]; Array[a, 75] (* _Robert G. Wilson v_ *)
%t A113605 nxt[{a_,b_,c_}]:={b,c,a+GCD[b,c]}; Transpose[NestList[nxt,{1,1,1},80]] [[1]] (* _Harvey P. Dale_, Sep 02 2015 *)
%K A113605 nonn
%O A113605 1,4
%A A113605 _Leroy Quet_, Jan 26 2006
%E A113605 More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Feb 01 2006