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A103794 Smallest number b such that b^Prime(n)-(b-1)^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)^p-x^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=n-1; cp=n^p-nm1^p; While[ !PrimeQ[cp], n=n+1; nm1=n-1; cp=n^p-nm1^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

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)