cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A330830 Numbers of the form (F_n-2)^2*F_n^2, where F_n is a Fermat prime, A019434. Also the first element of the power-spectral basis of A330829.

Original entry on oeis.org

9, 225, 65025, 4294836225, 18446744065119617025
Offset: 1

Views

Author

Walter Kehowski, Jan 06 2020

Keywords

Comments

The second element of the power-spectral basis of A330829 is A330831. We also have a(n) = (2^(2*2^n)-1)^2.

Examples

			a(1) = (3-2)^2*3^2  =9.
		

Crossrefs

Programs

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

Formula

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

A330828 The squares of the Fermat primes, (A019434(n))^2.

Original entry on oeis.org

9, 25, 289, 66049, 4295098369
Offset: 1

Views

Author

Walter Kehowski, Jan 06 2020

Keywords

Comments

Also the first element of the power-spectral basis of A330826. The second element of the power-spectral basis of A330826 is A001146(n+1), n=0..4.

Examples

			a(1) = 3^2 = 9. The spectral basis of A330826(1) = 12 is {9,4}, consisting of primes and powers.
		

Crossrefs

Programs

  • Maple
    F := n -> 2^(2^n) + 1;
    a := proc(n) if isprime(F(n)) then return F(n)^2 fi; end;
    [seq(a(n)),n=0..4)];
  • Mathematica
    (2^2^Select[Range[0,5],PrimeQ[2^(2^#)+1] &]+1)^2 (* Stefano Spezia, May 01 2025 *)

Formula

a(n) = A019434(n)^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

Views

Author

Walter Kehowski, Jan 06 2020

Keywords

Comments

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

Examples

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

Crossrefs

Programs

  • Maple
    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)];

Formula

a(n) = (F(n)^2 - 1)^2, where F(n) = 2^(2^n)+1 is a Fermat prime.
Showing 1-3 of 3 results.