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A187061
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Digits of the decimal expansion the constant whose continued fraction expansion is given by (a suffix of) A026465 (just start from the second term): [0;2,1,1,2,2,2,1,1,2,1,1,...]=0.3867499707....
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2
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3, 8, 6, 7, 4, 9, 9, 7, 0, 7, 1, 4, 3, 0, 0, 7, 0, 6, 1, 7, 1, 5, 2, 4, 8, 0, 3, 4, 8, 5, 5, 8, 0, 9, 3, 9, 6, 6, 1, 4, 4, 7, 6, 1, 5, 5, 6, 3, 0, 7, 7, 5, 0, 5, 1, 4, 7, 5, 0, 2, 8, 0, 5, 6, 8, 1, 2, 2, 4, 0, 7, 0, 7, 5, 8, 0, 5, 2, 9, 0, 9, 1
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OFFSET
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0,1
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COMMENTS
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Since the continued fraction of 0.3867499707... is a sequence which is the fixed point of a substitution, this constant is transcendental.
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LINKS
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MAPLE
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## period-doubling routine (see A026465):
double:=proc(SS)
NEW:=[op(S), op(S)]:
if op(nops(NEW), NEW)=1
then NEW:=[seq(op(j, NEW), j=1..nops(NEW)-2), op(nops(NEW)-1, NEW)+1]:
else NEW:=[seq(op(j, NEW), j=1..nops(NEW)-1), op(nops(NEW)-1, NEW)-1, 1]:
fi:
end proc:
# 10 loops of the above routine generate the first 1365 terms of the sequence
S:=[2]:
for j from 1 to 10 do S:=double(S); od:
## transform the list S into a continued fraction:
Digits:=500;
with(numtheory);
q:=evalf(invcfrac([[0], S]));
## list of digits:
L:=[seq(floor(q*10**j) - 10*floor(q*10**(j-1)), j=1..200)];
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MATHEMATICA
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First[RealDigits[FromContinuedFraction[ThueMorse[Range[550]]] - 1, 10, 100]] (* Paolo Xausa, Apr 04 2024 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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