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 A214523 #14 Apr 28 2014 15:12:23
%S A214523 13,53,107,643,7717,30869,432167,6050339,12100679,169409507,
%T A214523 9148113379,439109442193,5269313306317,84309012901073,
%U A214523 7587811161096571,303512446443862841,69807862682088453431,2652698781919361230379,143245734223645506440467
%N A214523 a(1) = 13, a(n) is smallest prime of the form k*a(n-1) + 1.
%C A214523 Sequence does not begin with a(1) = 2 or 3 (13 = 6*2+1 = 4*3*1; but 2*2+1 =5 or 2*3 +1 = 7 are smaller) , because this would be A061092 or A059411.
%H A214523 Harvey P. Dale, <a href="/A214523/b214523.txt">Table of n, a(n) for n = 1..300</a>
%e A214523 53 = 4*13 + 1 ; 107 = 2*53 + 1.
%t A214523 t = {13}; Do[k = 1; While[p = k*t[[-1]] + 1; ! PrimeQ[p], k++]; AppendTo[t, p], {20}]; t (* _T. D. Noe_, Jul 24 2012 *)
%t A214523 nxt[n_]:=Module[{k=1},While[!PrimeQ[k*n+1],k++];n*k+1]; NestList[nxt,13,20] (* _Harvey P. Dale_, Apr 28 2014 *)
%o A214523 (PARI) a=13;for(n=1,200,b=a*n+1;if(isprime(b),a=b;print1(a,", ");next(n=1)))
%Y A214523 Cf. A061092, A059411.
%K A214523 nonn
%O A214523 1,1
%A A214523 _Robin Garcia_, Jul 23 2012