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 A100276 #11 Mar 30 2024 15:27:22
%S A100276 3,5,7,11,13,17,19,23,59,71,73,83,89,97,191,337,359,433,569,617,643,
%T A100276 691,809,811,1439,1447,1451,1553,1571,1741,1993,2141,2339,2477,2693,
%U A100276 2791,2887,2917,4021,5039,5431,5581,5857,6353,6521,6529,6857,7211,7591,7883
%N A100276 a(0)=3; for n > 0, a(n) = smallest prime > a(n-1) such that Product_{i=0..n} a(i) - 2 is prime.
%H A100276 Harvey P. Dale, <a href="/A100276/b100276.txt">Table of n, a(n) for n = 0..100</a>
%e A100276 3*5-2=13 is prime;
%e A100276 3*5*7-2=103 is prime;
%e A100276 3*5*7*11-2=1153 is prime;
%e A100276 3*5*7*11*13-2=15013 is prime.
%t A100276 nxt[{pr_,a_}]:=Module[{p=NextPrime[a]},While[CompositeQ[pr*p-2],p=NextPrime[p]];{pr*p,p}]; NestList[nxt,{3,3},50][[;;,2]] (* _Harvey P. Dale_, Mar 30 2024 *)
%Y A100276 See A100277 for the resulting primes. Cf. A085013, A100301.
%K A100276 nonn
%O A100276 0,1
%A A100276 Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 29 2004
%E A100276 Corrected and extended by _Emeric Deutsch_, Mar 26 2005
%E A100276 More terms from _Ryan Propper_, Jan 11 2008