A162647 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A162647

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

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 * A368063 A364140 A358391

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