

A103794


Smallest number b such that b^prime(n)(b1)^prime(n) is prime.


4



2, 2, 2, 2, 6, 2, 2, 2, 6, 3, 2, 40, 7, 5, 13, 3, 3, 2, 7, 18, 47, 8, 6, 2, 26, 3, 42, 2, 13, 8, 2, 8, 328, 8, 9, 45, 27, 13, 76, 15, 52, 111, 5, 15, 50, 287, 16, 5, 40, 23, 110, 368, 23, 68, 28, 96, 81, 150, 3, 143, 4, 12, 403, 4, 45, 11, 83, 21, 96, 5, 109, 350, 128, 304, 38, 4, 163
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Conjecture: sequence is defined for all positive indices.
For p=prime(n), Eisenstein's irreducibility criterion can be used to show that the polynomial (x+1)^px^p is irreducible, which is a necessary (but not sufficient) condition for a(n) to exist.  T. D. Noe, Dec 05 2005


LINKS

Table of n, a(n) for n=1..77.


FORMULA

a(n) = A222119(n) + 1.  Ray Chandler, Feb 26 2017


EXAMPLE

2^prime(1)1^prime(1)=3 is prime, so a(1)=2;
2^prime(5)1^prime(5)=2047 has a factor of 23;
...
6^prime(5)5^prime(5)=313968931 is prime, so a(5)=6;


MATHEMATICA

Do[p=Prime[k]; n=2; nm1=n1; cp=n^pnm1^p; While[ !PrimeQ[cp], n=n+1; nm1=n1; cp=n^pnm1^p]; Print[n], {k, 1, 200}]


CROSSREFS

Cf. A103795, A066180, A058013, A222119.
Sequence in context: A292586 A324291 A114005 * A273258 A073124 A278260
Adjacent sequences: A103791 A103792 A103793 * A103795 A103796 A103797


KEYWORD

nonn


AUTHOR

Lei Zhou, Feb 24 2005


STATUS

approved



