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A237422
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Number of prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}, k < n.
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2
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0, 1, 2, 2, 1, 1, 1, 1, 0, 2, 0, 2, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 3, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,3
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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 (a Mersenne prime; see A000668).
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LINKS
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EXAMPLE
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a(2) = 1 because 2^2-(2*0+1)=3 and (2*0+1)*2^2-1=3 for k=0;
a(3) = 2 because 2^3-(2*0+1)=7 and (2*0+1)*2^3-1=7 for k=0, 2^3-(2*1+1)=5 and (2*1+1)*2^3-1=23 for k=1;
a(4) = 2 because 2^4-(2*1+1)=13 and (2*1+1)*2^4-1)=47 for k=1, 2^4-(2*2+1)=11 and (2*2+1)*2^4-1=59 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, 90] (* Giovanni Resta, Mar 04 2014 *)
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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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