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

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, 2, 48, 89, 30, 16, 147, 19, 19, 2, 16, 11, 289, 2, 12, 52, 2, 66, 9, 22, 5, 489, 69, 137, 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

Offset: 2

Author

Lei Zhou, Feb 23 2005

Keywords

• nonn

Comments

Conjecture: sequence is defined for any n>=2.

Examples

			(2^prime(2)+1)/(2+1) = 3 is prime, so a(2)=2;
(2^prime(10)+1)/(2+1) = 178956971 has a factor of 59;
(3^prime(10)+1)/(3+1) = 17157594341221 has a factor of 523;
...
(7^prime(10)+1)/(7+1) = 402488219476647465854701 is prime, so a(10)=7.
		

Crossrefs

Cf. A056993, A066180, A085398.

Programs

Mathematica

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}]

Formula

a(n) = A085398(2*prime(n)) for n >= 2. - Jinyuan Wang, Dec 17 2022