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A215050
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Number of primes of the form 1 + b^16 for 1 < b < 10^n.
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12
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OFFSET
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1,2
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COMMENTS
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Primes 1 + b^16 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.229464*li(10^n).
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1 because the only Fermat prime F_4(b) where b<10^1 is the prime 65537.
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MATHEMATICA
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Table[Length[Select[Range[2, 10^n-1]^16 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
Module[{nn=8, t}, t=Table[If[PrimeQ[n^16+1], 1, 0], {n, 2, 10^nn}]; Table[Total[ Take[t, 10^i-1]], {i, nn}]] (* Harvey P. Dale, Sep 14 2015 *)
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PROG
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(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^16+1))
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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