A187061 - OEIS

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

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OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..81.

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

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