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A162634 Numerators of fractions with denominators A000215(n) approximating the Thue-Morse constant 1
1, 2, 7, 106, 27031, 1771476586, 7608434000728254871, 140350834813144189858090274002849666666, 47758914269546354982683078068829456704164423862093743397580034411621752859031 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
FORMULA
a(1)=2, and, for n>=2, a(n) = 1 + (2^(2^(n-1))-1) * a(n-1).
PROG
(PARI) a(n)=if(n<=1, [1, 2][n+1], 1+(2^(2^(n-1))-1)*a(n-1)); /* Joerg Arndt, Mar 11 2013 */
CROSSREFS
Sequence in context: A122524 A229165 A307329 * A235470 A072664 A352046
KEYWORD
nonn,uned
AUTHOR
Vladimir Shevelev, Jul 08 2009, Jul 14 2009
EXTENSIONS
Added more terms, Joerg Arndt, Mar 11 2013
STATUS
approved

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Last modified February 24 05:49 EST 2024. Contains 370293 sequences. (Running on oeis4.)