cp's OEIS Frontend

A103795 Minimal base b such that (b^prime(n)+1)/(b+1) is prime.

%I A103795 #8 Dec 17 2022 08:23:09
%S A103795 2,2,2,2,2,2,2,2,7,2,16,61,2,6,10,6,2,5,46,18,2,49,16,70,2,5,6,12,92,
%T A103795 2,48,89,30,16,147,19,19,2,16,11,289,2,12,52,2,66,9,22,5,489,69,137,
%U A103795 16,36,96,76,117,26,3,159,10,16,209,2,16,23,273,2,460,22,3,36,28,329,43,69,86
%N A103795 Minimal base b such that (b^prime(n)+1)/(b+1) is prime.
%C A103795 Conjecture: sequence is defined for any n>=2.
%F A103795 a(n) = A085398(2*prime(n)) for n >= 2. - _Jinyuan Wang_, Dec 17 2022
%e A103795 (2^prime(2)+1)/(2+1) = 3 is prime, so a(2)=2;
%e A103795 (2^prime(10)+1)/(2+1) = 178956971 has a factor of 59;
%e A103795 (3^prime(10)+1)/(3+1) = 17157594341221 has a factor of 523;
%e A103795 ...
%e A103795 (7^prime(10)+1)/(7+1) = 402488219476647465854701 is prime, so a(10)=7.
%t A103795 Do[p=Prime[k]; n=2; cp=(n^p+1)/(n+1); While[ !PrimeQ[cp], n=n+1; cp=(n^p+1)/(n+1)]; Print[n], {k, 2, 200}]
%Y A103795 Cf. A056993, A066180, A085398.
%K A103795 nonn
%O A103795 2,1
%A A103795 _Lei Zhou_, Feb 23 2005