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 A215047 Number of primes of the form 1 + b^2 for 1 < b < 10^n. 13
 3, 18, 111, 840, 6655, 54109, 456361, 3954180, 34900212, 312357933, 2826683629, 25814570671 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A083844, A206709. Sequence in context: A000274 A207321 A193236 * A213099 A199259 A163471 Adjacent sequences:  A215044 A215045 A215046 * A215048 A215049 A215050 KEYWORD nonn,more AUTHOR Henryk Dabrowski, Aug 01 2012 STATUS approved

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Last modified January 28 13:29 EST 2020. Contains 331321 sequences. (Running on oeis4.)