A185981 a(n) = 2^(2*(5^(n-1) - 1)).

1, 256, 281474976710656, 452312848583266388373324160190187140051835877600158453279131187530910662656

Offset: 1

Author

Wolfdieter Lang, Feb 24 2011

Keywords

• nonn
• easy

Comments

The number of digits of a(n) is 1, 3, 15, 75, 376, 1881, 9407, 47036, 235180, 1175898, ....

-1/(4*a(n)) is the coefficient of x^0 of the minimal polynomial Psi(5^n,x) of cos(2*Pi/5^n). Hence 4*a(n)*Psi(5^n,x) is the integer polynomial with coefficient -1 of x^0. E.g., Psi(5,1)= x^2 + (1/2)*x -1/4, Psi(25,x)= x^10 + ... -1/1024. See A181875/A181876, A181877 and the W. Lang link under A181875.

Links

• Index to divisibility sequences

Crossrefs

Cf. A023365.

Programs

Magma

[(2^(2*(5^((n-1)))-1)/2): n in [1..5]]; // Vincenzo Librandi, Apr 19 2011

Mathematica

Table[2^(2*(5^(n-1)-1)), {n,1,10}] (* G. C. Greubel, Jul 24 2017 *)

PARI

a(n)=1<<(2*(5^(n-1)-1)) \\ Charles R Greathouse IV, Jan 13 2012

Formula

a(n) = 2^(2*(5^(n-1) - 1)).