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 A215048 Number of primes of the form 1 + b^4 for 1 < b < 10^n. 13
 3, 17, 110, 789, 6395, 52610, 445868, 3857543, 34057327 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A214452. Sequence in context: A103730 A074556 A295808 * A119259 A249921 A174404 Adjacent sequences:  A215045 A215046 A215047 * A215049 A215050 A215051 KEYWORD nonn AUTHOR Henryk Dabrowski, Aug 01 2012 STATUS approved

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Last modified July 30 15:29 EDT 2021. Contains 346359 sequences. (Running on oeis4.)