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 A083566 #13 Jul 10 2023 11:51:32
%S A083566 1,3,5,7,9,15,19,25,27,53,57,65,71,87,101,151,195,247,253,255,277,289,
%T A083566 291,301,321,355,361,443,455,461,491,531,533,541,599,603,619,635,647,
%U A083566 667,805,817,871,1003,1011,1179,1205,1223,1327,1357,1531,1551,1603,1619
%N A083566 a(1) = 1; for n>1, a(n) = smallest odd number > a(n-1) such that a(1)*...*a(n) + 2 is a prime.
%H A083566 Harvey P. Dale, <a href="/A083566/b083566.txt">Table of n, a(n) for n = 1..200</a>
%t A083566 a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 2}, While[ !PrimeQ[k*Times @@ Table[a[i], {i, 1, n - 1}] + 2], k += 2]; k]; Table[ a[n], {n, 1, 54}]
%t A083566 nxt[{pr_,a_}]:=Module[{k=a+2},While[!PrimeQ[pr k+2],k=k+2];{pr k,k}]; NestList[nxt,{1,1},60][[;;,2]] (* _Harvey P. Dale_, Jul 10 2023 *)
%Y A083566 Cf. A084723, A084724, A084725, A085013.
%K A083566 nonn
%O A083566 1,2
%A A083566 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003
%E A083566 Edited and extended by _Robert G. Wilson v_, Jun 17 2003
%E A083566 Edited by _N. J. A. Sloane_, Nov 01 2008 at the suggestion of R. J. Mathar