login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A237422
Number of prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}, k < n.
2
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
OFFSET
1,3
COMMENTS
If k = 0, then the two numbers in the "prime pair" are actually the same number, 2^n - 1 (a Mersenne prime; see A000668).
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A054535 A054534 A085769 * A102552 A131341 A124034
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(6), a(42), a(48)-a(87) from Giovanni Resta, Mar 04 2014
STATUS
approved