OFFSET
1,1
COMMENTS
Primes 1 + b^4 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.66974*li(10^n).
REFERENCES
Daniel Shanks, On Numbers of the Form n^4 + 1, Math. Comput. 15 (1961), 186-189.
LINKS
Yves Gallot, How many prime numbers appear in a sequence ?
FORMULA
a(n) = A214452(4*n) - 1.
EXAMPLE
a(1) = 3 because the only generalized Fermat primes F_2(b) where b<10^1 are the primes: 17, 257, 1297.
MATHEMATICA
Table[Length[Select[Range[2, 10^n-1]^4 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
PROG
(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^4+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Henryk Dabrowski, Aug 01 2012
STATUS
approved