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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.
1
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
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved