OFFSET
0,1
COMMENTS
Bisection of A003010.
a(4) has 147 digits and a(5) has 586 digits. - Harvey P. Dale, Mar 03 2020
FORMULA
Let alpha = 2 + sqrt(3). Then a(n) = (alpha)^(4^n) + (1/alpha)^(4^n).
Product_{n >= 0} ((1 + 2/a(n))/(1 - 2/a(n)^2)) = sqrt(3).
From Peter Bala, Dec 06 2022: (Start)
a(n) = 2*T(4^n,2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind.
Let b(n) = a(n) - 4. The sequence {b(n)} appears to be a strong divisibility sequence, that is, gcd(b(n),b(m)) = b(gcd(n,m)) for n, m >= 1. (End)
MATHEMATICA
NestList[#^4-4#^2+2&, 4, 5] (* Harvey P. Dale, Mar 03 2020 *)
PROG
(PARI) a(n)={if(n==0, 4, a(n-1)^4-4*a(n-1)^2+2)} \\ Edward Jiang, Sep 11 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Nov 13 2012
STATUS
approved