login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162634 Numerators of fractions with denominators A000215(n) approximating the Thue-Morse constant 1

%I

%S 1,2,7,106,27031,1771476586,7608434000728254871,

%T 140350834813144189858090274002849666666,

%U 47758914269546354982683078068829456704164423862093743397580034411621752859031

%N Numerators of fractions with denominators A000215(n) approximating the Thue-Morse constant

%C One can prove that if in the sequence of numbers N for which A010060(N+2^n)= A010060(N) you replace the odious (evil) terms by 1's (0's), then we obtain 2^(n+1)-periodic (0,1)-sequence; if you write it in the form .xx...,i.e., as a binary infinite fraction, then the corresponding fraction has the form a(n)/A000215(n). These fractions very fast converge to the Thue-Morse constant .4124540336401...; e.g a(5)/(2^32+1) approximates this constant up to 10^(-9). These approximations differ from A074072-A074073. Conjecture. For n>=1, the fraction a(n)/A000215(n) is a convergent corresponding to the continued fraction for the Thue-Morse constant.

%H V. Shevelev, <a href="http://arXiv.org/abs/0907.0880">Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence</a>,

%F a(1)=2, and, for n>=2, a(n) = 1 + (2^(2^(n-1))-1) * a(n-1).

%o (PARI) a(n)=if(n<=1, [1,2][n+1], 1+(2^(2^(n-1))-1)*a(n-1)); /* _Joerg Arndt_, Mar 11 2013 */

%Y Cf. A010060, A000215, A085394, A085395, A081706, A161627, A161639, A074072, A074073.

%K nonn,uned

%O 0,2

%A _Vladimir Shevelev_, Jul 08 2009, Jul 14 2009

%E Added more terms, _Joerg Arndt_, Mar 11 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 01:15 EST 2019. Contains 329977 sequences. (Running on oeis4.)