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A215047
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Number of primes of the form 1 + b^2 for 1 < b < 10^n.
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14
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3, 18, 111, 840, 6655, 54109, 456361, 3954180, 34900212, 312357933, 2826683629, 25814570671, 237542444179, 2199894223891
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3 because the only generalized Fermat primes F_1(b) where b < 10^1 are the primes: 5, 17, 37.
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MATHEMATICA
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Table[Length[Select[Range[2, 10^n-1]^2 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
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PROG
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(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^2+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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