|
%I #16 Mar 12 2020 21:15:04
%S 3,8,9,7,0,8,0,9,8,8,3,8,9,5,4,8,9,7,2,3,3,8,2,6,9,6,4,0,7,7,6,5,2,2,
%T 2,6,0,7,1,0,9,4,2,8,4,9,0,5,8,0,1,8,3,6,6,9,6,3,6,8,2,7,8,5,2,0,4,4,
%U 3,5,1,8,9,7,0,0,2,2,1,3,1,3,6,3,9,1,7,6,1,5,8,8,2,4,3,3,1,5,7,2,1,5,9,1,9,6
%N Decimal expansion of x such that Sum_{k>=1} x^Fibonacci(k) = 1.
%e 0.3897080988389....
%t digits = 106; Clear[f];
%t f[m_] := f[m] = Module[{s}, s[c_?NumericQ] := NSum[c^Fibonacci[k], {k, 1, m}, WorkingPrecision -> digits];c /. FindRoot[s[c] == 1, {c, 1/2}, WorkingPrecision -> digits] // RealDigits // First];
%t f[1]; f[m = 2];
%t While[f[m] != f[m/2], m = 2 m; Print["m = ", m]];
%t f[m] (* _Jean-François Alcover_, Mar 11 2020 *)
%Y Cf. A000045, A084119.
%K cons,nonn
%O 0,1
%A _Benoit Cloitre_, Jan 26 2003
%E More terms from _Jon E. Schoenfield_, Mar 11 2018
|
