A330826 Numbers of the form 2^((2^n)+1)*F_n, where F_n is a Fermat prime, A019434.

12, 40, 544, 131584, 8590065664

Offset

1,1

Comments

Also numbers with power-spectral basis {F_n^2, (F_n-1)^2}.

The first factor of a(n) is 2^A000051(n). The first element of the power-spectral basis of a(n) is A001146, and the second element is A330828.

Links

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

Formula

a(n) =2^A000051(n)*A019434(n).

Example

a(2) = 2^(2+1)*5 = 40, and the spectral basis of 40 is {25,16}, consisting of primes and powers.

Maple

F := n -> 2^(2^n)+1;
a := proc(n) if isprime(F(n)) then return 2^((2^n)+1)*F(n) fi; end;

Crossrefs

Cf. A001146, A000215, A019434, A000051, A330828.

Sequence in context: A180093 A137389 A228203 * A222806 A375804 A251429

Adjacent sequences: A330823 A330824 A330825 * A330827 A330828 A330829

Keyword

nonn,hard,more

Author

Walter Kehowski, Jan 06 2020

Status

approved