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%I #25 Aug 13 2012 16:19:11
%S 2,2,40,335,2498,20886,174368,1507722,13300713
%N Number of primes of the form 1 + b^8 for 1 < b < 10^n.
%C Primes 1 + b^8 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.261599*li(10^n).
%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">Status of the smallest base values yielding Generalized Fermat primes</a>
%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/stat.html">How many prime numbers appear in a sequence ?</a>
%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/ccdgfpn.html">A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)</a>
%F a(n) = A214454(8*n) - 1.
%e a(1) = 2 because the only Fermat primes F_3(b) where b<10^1 are the primes: 257, 65537.
%t Table[Length[Select[Range[2,10^n-1]^8 + 1, PrimeQ]], {n, 5}] (* _T. D. Noe_, Aug 01 2012 *)
%o (PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^8+1))
%Y Cf. A214454.
%K nonn
%O 1,1
%A _Henryk Dabrowski_, Aug 01 2012
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