A239323 Semiprimes of the form (2^n + 1)*(2^n - n + 1).

4, 6, 15, 221, 4294049777

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 15 2014

Keywords

• nonn

Comments

Generated by n: 0, 1, 2, 4, 16, ...

The positions of a(n) in A001358: 1, 2, 6, 75, ...

Examples

			4 is in this sequence because (2^0 + 1)*(2^0 - 0 + 1) = 2*2 = 4 is semiprime for n = 0,
6 is in this sequence because (2^1 + 1)*(2^1 - 1 + 1) = 3*2 = 6 is semiprime for n = 1,
15 is in this sequence because (2^2 + 1)*(2^2 - 2 + 1) = 5*3 = 15 is semiprime for n = 2.
		

Crossrefs

Cf. A019434, A100361, A100362.

Programs

Magma

k := 1;
     for n in [1..10000] do
        if IsPrime(k*2^n + 1) and IsPrime(k*2^n - n + 1) then
           (k*2^n + 1)*(k*2^n - n + 1);
        end if;
     end for;

Mathematica

Select[Table[(2^n+1)(2^n-n+1),{n,0,20}],PrimeOmega[#]==2&] (* Harvey P. Dale, May 11 2024 *)