A247950 Decimal expansion of the value of a nonregular continued fraction giving tau/(3*tau-1), where tau is the Prouhet-Thue-Morse constant.

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

Offset: 1

Author

Jean-François Alcover, Oct 01 2014

Keywords

• nonn
• cons

Examples

			1.737657494776553621260067888517462099794385624106538329626...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse Constant, p. 437.

Links

• Eric Weisstein's MathWorld, Thue-Morse Constant

Crossrefs

Cf. A010060, A014571, A058631.

Programs

Maple

evalf(1/(3-1/(1/2-(1/4)*(product(1-1/2^(2^k), k=0..11)))), 120); # Vaclav Kotesovec, Oct 01 2014

Mathematica

(* 10 terms suffice to get 103 correct digits *) t = Fold[Function[2^2^#2 - (2^2^#2 - 1)/#1], 2, Reverse[Range[0, 10]]]; RealDigits[t, 10, 103] // First

Formula

2 - 1/(4 - 3/(16 - 15/(256 - 255/65536 - ...))).

Pattern is generated by 2^(2^n) and 2^(2^n)-1.