A395973 - OEIS

%I #9 May 28 2026 13:09:28

%S 1,6,3,2,0,5,1,6,6,9,8,4,7,5,7,7,4,8,7,6,7,4,0,6,2,6,1,7,2,1,3,5,7,7,

%T 3,9,9,0,6,1,8,5,9,0,6,7,5,4,2,3,3,0,3,4,6,3,0,9,1,0,9,5,4,1,3,5,8,0,

%U 2,4,2,8,7,4,0,2,5,2,2,2,9,8,2,7,0,8,5,0

%N Decimal expansion of the solution of phi^(2*x)*cos(Pi*x) = (27 + 7*sqrt(5))/22, where phi = (1 + sqrt(5)) / 2.

%C The first real root of the function defining A396201. See the illustration given there. The root is almost certainly transcendental.

%e 1.632051669847577487674062617213577399061859...

%o (Python)

%o import mpmath

%o mpmath.mp.dps = 105

%o root = guess = 1.63

%o phi = (1 + mpmath.sqrt(5)) / 2

%o rhs = (27 + 7 * mpmath.sqrt(5)) / 22

%o f = lambda x: phi**(2*x) * mpmath.cos(mpmath.pi * x) - rhs

%o try:

%o     root = mpmath.findroot(f, guess)

%o except ValueError as e:

%o     root = 0

%o root_str = str(root)

%o ",".join(char for char in root_str if char.isdigit())

%Y Cf. A001622, A396201.

%K nonn,cons

%O 1,2

%A _Peter Luschny_, May 27 2026