cp's OEIS Frontend

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....

%I A187061 #28 Apr 04 2024 17:25:31
%S A187061 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,
%T A187061 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,
%U A187061 4,0,7,0,7,5,8,0,5,2,9,0,9,1
%N 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....
%C A187061 Since the continued fraction of 0.3867499707... is a sequence which is the fixed point of a substitution, this constant is transcendental.
%H A187061 Claudio Bonanno, Carlo Carminati, Stefano Isola, and Giulio Tiozzo, <a href="https://arxiv.org/abs/1012.2131">Dynamics of continued fractions and kneading sequences of unimodal maps</a>, arXiv:1012.2131 [math.DS], 2010-2012.
%H A187061 Julien Cassaigne, <a href="https://doi.org/10.1016/S0304-3975(98)00247-3">Limit values of the recurrence quotient of Sturmian sequences</a>, Theoret. Comput. Sci., Vol. 218, No. 1 (1999), pp. 3-12.
%H A187061 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%p A187061 ## period-doubling routine (see A026465):
%p A187061 double:=proc(SS)
%p A187061 NEW:=[op(S), op(S)]:
%p A187061 if op(nops(NEW), NEW)=1
%p A187061 then NEW:=[seq(op(j, NEW), j=1..nops(NEW)-2), op(nops(NEW)-1, NEW)+1]:
%p A187061 else NEW:=[seq(op(j, NEW), j=1..nops(NEW)-1), op(nops(NEW)-1, NEW)-1, 1]:
%p A187061 fi:
%p A187061 end proc:
%p A187061 # 10 loops of the above routine generate the first 1365 terms of the sequence
%p A187061 S:=[2]:
%p A187061 for j from 1 to 10  do S:=double(S); od:
%p A187061 ## transform the list S into a continued fraction:
%p A187061 Digits:=500;
%p A187061 with(numtheory);
%p A187061 q:=evalf(invcfrac([[0],S]));
%p A187061 ## list of digits:
%p A187061 L:=[seq(floor(q*10**j) - 10*floor(q*10**(j-1)), j=1..200)];
%t A187061 First[RealDigits[FromContinuedFraction[ThueMorse[Range[550]]] - 1, 10, 100]] (* _Paolo Xausa_, Apr 04 2024 *)
%Y A187061 Cf. A026465.
%K A187061 nonn,cons,easy
%O A187061 0,1
%A A187061 _Carlo Carminati_, Mar 03 2011