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 A217663 #19 May 19 2018 17:36:55
%S A217663 1,3,1,5,3,7,1,3,5,11,1,13,7,5,1,17,3,19,5,1,11,23,1,5,13,1,1,29,5,31,
%T A217663 1,11,17,1,1,37,19,13,1,41,1,43,11,1,23,47,1,1,5,17,13,53,1,1,1,1,29,
%U A217663 59,1,61,31,1,1,13,11,67,17,23,1,71,1,73,37,1,1
%N A217663 a(n) = A217662(n+2)/A217662(n) - 1, n > 0.
%C A217663 a(prime(n)-1) = prime(n) for n>1, so this sequence includes all odd primes. - _Jon Perry_, Oct 10 2012, edited & corrected by _M. F. Hasler_, Oct 11 2012
%t A217663 RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1]==2,a[2]==2},a{n,3,51}] /RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1]==2,a[2]==2},a,{n,1,49}]-1
%t A217663 t = {2, 2}; Do[AppendTo[t, t[[-2]] + LCM[n - 1, t[[-2]]]], {n, 3, 100}]; Drop[t, 2]/Drop[t, -2] - 1 (* _T. D. Noe_, Oct 10 2012 *)
%Y A217663 Cf. A135504, A217662.
%K A217663 nonn
%O A217663 1,2
%A A217663 _Pedja Terzic_, Oct 10 2012