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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
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
Sequence in context: A292586 A324291 A114005 * A273258 A073124 A278260
KEYWORD
nonn
AUTHOR
Lei Zhou, Feb 24 2005
STATUS
approved

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Last modified February 21 03:46 EST 2024. Contains 370219 sequences. (Running on oeis4.)