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

4, 6, 15, 221, 4294049777

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..5.

Example

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.

Mathematica

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

Prog

(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;

Crossrefs

Cf. A019434, A100361, A100362.

Sequence in context: A191311 A086714 A356801 * A009463 A066260 A248591

Adjacent sequences: A239320 A239321 A239322 * A239324 A239325 A239326

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 15 2014

Status

approved