A187061 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....

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

Offset: 0

Author

Carlo Carminati, Mar 03 2011

Keywords

• nonn
• cons
• easy

Comments

Since the continued fraction of 0.3867499707... is a sequence which is the fixed point of a substitution, this constant is transcendental.

Links

• Claudio Bonanno, Carlo Carminati, Stefano Isola, and Giulio Tiozzo, Dynamics of continued fractions and kneading sequences of unimodal maps, arXiv:1012.2131 [math.DS], 2010-2012.
• Julien Cassaigne, Limit values of the recurrence quotient of Sturmian sequences, Theoret. Comput. Sci., Vol. 218, No. 1 (1999), pp. 3-12.
• Index entries for transcendental numbers

Crossrefs

Cf. A026465.

Programs

Maple

## 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)];

Mathematica

First[RealDigits[FromContinuedFraction[ThueMorse[Range[550]]] - 1, 10, 100]] (* Paolo Xausa, Apr 04 2024 *)