

A103795


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


11



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
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OFFSET

2,1


COMMENTS

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


LINKS

Table of n, a(n) for n=2..78.


EXAMPLE

(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.


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}]


CROSSREFS

Cf. A066180, A056993.
Sequence in context: A307590 A307987 A047935 * A123627 A171818 A248777
Adjacent sequences: A103792 A103793 A103794 * A103796 A103797 A103798


KEYWORD

nonn


AUTHOR

Lei Zhou, Feb 23 2005


STATUS

approved



