A111671 Smallest prime p > 3 such that p-1 has a prime factor > (p-1)^(n/(n+1)).

7, 11, 23, 47, 83, 167, 263, 563, 1187, 2063, 4127, 8423, 16487, 32843, 65543, 131267, 262643, 524387, 1048703, 2097779, 4195259, 8389163, 16777907, 33554519, 67109543, 134217827, 268436867, 536871263, 1073742623, 2147483783, 4294967387, 8589935363, 17179869263, 34359739319

Offset: 1

Author

Rick L. Shepherd, Aug 15 2005

Keywords

• nonn

Comments

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.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..36

Crossrefs

Cf. A111668, A005385 (safe primes).

Programs

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};
a111671(10^7) \\ Hugo Pfoertner, Dec 12 2023

Extensions

a(28)-a(34) from Hugo Pfoertner, Dec 12 2023