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

1,2

References

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

Links

Table of n, a(n) for n=1..103.

Eric Weisstein's MathWorld, Thue-Morse Constant

Formula

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

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

Example

1.737657494776553621260067888517462099794385624106538329626...

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

Crossrefs

Cf. A010060, A014571, A058631.

Sequence in context: A160578 A244258 A271178 * A256844 A346538 A166201

Adjacent sequences: A247947 A247948 A247949 * A247951 A247952 A247953

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 01 2014

Status

approved