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 A111671 #11 Dec 13 2023 14:46:02
%S A111671 7,11,23,47,83,167,263,563,1187,2063,4127,8423,16487,32843,65543,
%T A111671 131267,262643,524387,1048703,2097779,4195259,8389163,16777907,
%U A111671 33554519,67109543,134217827,268436867,536871263,1073742623,2147483783,4294967387,8589935363,17179869263,34359739319
%N A111671 Smallest prime p > 3 such that p-1 has a prime factor > (p-1)^(n/(n+1)).
%C A111671 a(1) = 7 = A111668(1). Conjectures: (1) This is a subsequence of the safe primes (A005385), (2) lim{n --> oo}(a(n+1)/a(n)) = 2.
%H A111671 Hugo Pfoertner, <a href="/A111671/b111671.txt">Table of n, a(n) for n = 1..36</a>
%o A111671 (PARI) a111671(plimit) = {my (n=1, L=List()); forprime (p=5, plimit, my (x=(p-1)^(n/(n+1)), F=factor(p-1), mF=F[#F[,2],1]); if (mF>x, listput(L,p); n++)); L};
%o A111671 a111671(10^7) \\ _Hugo Pfoertner_, Dec 12 2023
%Y A111671 Cf. A111668, A005385 (safe primes).
%K A111671 nonn
%O A111671 1,1
%A A111671 _Rick L. Shepherd_, Aug 15 2005
%E A111671 a(28)-a(34) from _Hugo Pfoertner_, Dec 12 2023