A330830 -id:A330830 - cp's OEIS frontend

A330829 Numbers of the form 2^(2(2^n)+1)F_n^2, where F_n is a Fermat prime A019434.

72, 800, 147968, 8657174528, 36894614055915880448

Offset: 0

Walter Kehowski, Jan 06 2020

nonn

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

The first element of the power-spectral basis of a(n) is A330830, and the second element is A330831. The first factor of a(n) is A000051(n) and the second factor is A330828.

			a(0) = 2^(2+1)*(2+1)^2 = 72, and the spectral basis is {(3-2)^2*3^2, (3^2-1)^2} = {9,64}, consisting of powers.

Cf. A000215, A001146, A019434, A000051, A330828, A330830, A330831.

F := proc(n) return 2^(2^n)+1 end;
G := proc(n) return 2^(2*(2^n)+1) end;
a := proc(n) if isprime(F(n)) then return G(n)*F(n)^2 fi; end;
[seq(a(n),n=0..4)];

a(n) = 2^(2*(2^n)+1)*(2^(2^n)+1)^2.

A330831 a(n) = (F_n^2 - 1)^2, where F_n is a Fermat prime, A019434.

Original entry on oeis.org

64, 576, 82944, 4362338304, 18447869990796263424

Offset: 1

Walter Kehowski, Jan 06 2020

nonn

Also the second element of the power-spectral basis of A330829.

The first element of the power-spectral basis of A330829 is A330830.

			a(0) = (3^2 - 1)^2 = 64.

Cf. A000215, A001146, A019434, A330827, A330828, A330829, A330830.

F := proc(n) return 2^(2^n)+1 end;
a := proc(n) if isprime(F(n)) then return (F(n)^2-1)^2 fi; end;
[seq(a(n),n=0..4)];

a(n) = (F(n)^2 - 1)^2, where F(n) = 2^(2^n)+1 is a Fermat prime.

cp's OEIS Frontend

A330829 Numbers of the form 2^(2(2^n)+1)F_n^2, where F_n is a Fermat prime A019434.

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A330831 a(n) = (F_n^2 - 1)^2, where F_n is a Fermat prime, A019434.

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cp's OEIS Frontend

A330829 Numbers of the form 2^(2*(2^n)+1)*F_n^2, where F_n is a Fermat prime A019434.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Formula

A330831 a(n) = (F_n^2 - 1)^2, where F_n is a Fermat prime, A019434.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Formula

A330829 Numbers of the form 2^(2(2^n)+1)F_n^2, where F_n is a Fermat prime A019434.