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COMMENTS
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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.
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