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