A111671 - OEIS

%I #11 Dec 13 2023 14:46:02

%S 7,11,23,47,83,167,263,563,1187,2063,4127,8423,16487,32843,65543,

%T 131267,262643,524387,1048703,2097779,4195259,8389163,16777907,

%U 33554519,67109543,134217827,268436867,536871263,1073742623,2147483783,4294967387,8589935363,17179869263,34359739319

%N Smallest prime p > 3 such that p-1 has a prime factor > (p-1)^(n/(n+1)).

%C 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 Hugo Pfoertner, <a href="/A111671/b111671.txt">Table of n, a(n) for n = 1..36</a>

%o (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(10^7) \\ _Hugo Pfoertner_, Dec 12 2023

%Y Cf. A111668, A005385 (safe primes).

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Aug 15 2005

%E a(28)-a(34) from _Hugo Pfoertner_, Dec 12 2023