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A238735
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Number of prime pairs {2^n + (2k + 1), (2k + 1)*2^n + 1}, k < n.
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1
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1, 2, 1, 2, 0, 3, 2, 2, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 3, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,2
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COMMENTS
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If k = 0, then the two numbers in the "prime pair" are actually the same number, 2^n + 1 (which is either 2 or a Fermat prime; see A019434, A092506).
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LINKS
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EXAMPLE
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a(1) = 1 because 2^1+(2*0+1)=3 and (2*0+1)*2^1+1=3 is prime pair for k=0,
a(2) = 2 because 2^2+(2*0+1)=5 and (2*0+1)*2^2+1=5 is prime pair for k=0, 2^2+(2*1+1)=7 and (2*1+1)*2^2+1=13 is prime pair for k=1,
a(3) = 1 because 2^3+(2*2+1)=13 and (2*2+1)*2^3+1=41 is prime pair for k=2.
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MATHEMATICA
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a[n_] := Length@Select[Range[0, n-1], PrimeQ[2^n + (2*# + 1)] && PrimeQ[(2*# + 1)*2^n + 1] &]; Array[a, 100] (* Giovanni Resta, Mar 04 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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