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A162647 Numerators associated with denominators A000215(n) approximating the complementary Thue-Morse constant. 0
2, 3, 10, 151, 38506, 2523490711, 10838310072981296746, 199931532107794273605284333428918544791, 68033174967769840440887906939858451149105560803546820641877549596291376780906 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If in the sequence of numbers N for which A010060(N+2^n)=1-A010060(N) the odious (evil) terms are

replaced by 1's (0's), we obtain a 2^(n+1)-periodic binary sequence. These are the post-period

binary (base-2) digits of the complementary Thue-Morse constant 1-A014571 = 0.58754596635989240221663...,

which has a continued fraction and convergents 3/5, 7/12, 10/17, 47/80, 151/257, 801/1365,...

The a(n) are numerators of the convergents selected with denominators taken from A000215.

LINKS

Table of n, a(n) for n=0..8.

V. Shevelev, Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence, arXiv:0907.0880

FORMULA

a(n)=A000215(n)-A162634(n). For n>=1, a(n+1)=1+(2^(2^n)-1)*a(n) = 1+A051179(n)*a(n).

CROSSREFS

Cf. A010060, A000215, A085394, A085395, A081706, A161627, A161639, A162634.

Sequence in context: A064647 A119810 A055708 * A132536 A322067 A302250

Adjacent sequences:  A162644 A162645 A162646 * A162648 A162649 A162650

KEYWORD

nonn,frac

AUTHOR

Vladimir Shevelev, Jul 08 2009, Jul 14 2009

EXTENSIONS

Edited by R. J. Mathar, Sep 23 2009

STATUS

approved

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Last modified January 26 07:38 EST 2022. Contains 350577 sequences. (Running on oeis4.)