OFFSET
1,1
COMMENTS
Primes 1 + b^2 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.6864067*li(10^n).
LINKS
Yves Gallot, How many prime numbers appear in a sequence ?
Daniel Shanks, On the Conjecture of Hardy & Littlewood concerning the Number of Primes of the Form n^2 + a, Math. Comp. 14 (1960), 320-332.
FORMULA
a(n) = A083844(2*n) - 1.
EXAMPLE
a(1) = 3 because the only generalized Fermat primes F_1(b) where b < 10^1 are the primes: 5, 17, 37.
MATHEMATICA
Table[Length[Select[Range[2, 10^n-1]^2 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
PROG
(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^2+1))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Henryk Dabrowski, Aug 01 2012
EXTENSIONS
a(13)-a(14) from Jinyuan Wang, Feb 23 2020
STATUS
approved