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a(n) = 2^(2*(5^(n-1) - 1)).
0

%I #19 Sep 08 2022 08:45:55

%S 1,256,281474976710656,

%T 452312848583266388373324160190187140051835877600158453279131187530910662656

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

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

%C -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.

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

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

%t Table[2^(2*(5^(n-1)-1)), {n,1,10}] (* _G. C. Greubel_, Jul 24 2017 *)

%o (Magma) [(2^(2*(5^((n-1)))-1)/2): n in [1..5]]; // _Vincenzo Librandi_, Apr 19 2011

%o (PARI) a(n)=1<<(2*(5^(n-1)-1)) \\ _Charles R Greathouse IV_, Jan 13 2012

%Y Cf. A023365.

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Feb 24 2011