A162647 Numerators associated with denominators A000215(n) approximating the complementary Thue-Morse constant.

2, 3, 10, 151, 38506, 2523490711, 10838310072981296746, 199931532107794273605284333428918544791, 68033174967769840440887906939858451149105560803546820641877549596291376780906

Offset: 0

Author

Vladimir Shevelev, Jul 08 2009, Jul 14 2009

Keywords

• nonn
• frac

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

• 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

Crossrefs

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

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).

Extensions

Edited by R. J. Mathar, Sep 23 2009