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A247950 Decimal expansion of the value of a nonregular continued fraction giving tau/(3*tau-1), where tau is the Prouhet-Thue-Morse constant. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A166201 A248281

Adjacent sequences:  A247947 A247948 A247949 * A247951 A247952 A247953

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Oct 01 2014

STATUS

approved

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Last modified July 18 10:35 EDT 2019. Contains 325138 sequences. (Running on oeis4.)