A079591 Decimal expansion of x such that Sum_{k>=1} x^Fibonacci(k) = 1.

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, 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, 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

Offset: 0

Author

Benoit Cloitre, Jan 26 2003

Keywords

• cons
• nonn

Examples

			0.3897080988389....
		

Crossrefs

Cf. A000045, A084119.

Programs

Mathematica

digits = 106; Clear[f];
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];
f[1]; f[m = 2];
While[f[m] != f[m/2], m = 2 m; Print["m = ", m]];
f[m] (* Jean-François Alcover, Mar 11 2020 *)

Extensions

More terms from Jon E. Schoenfield, Mar 11 2018