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 A153778 Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation. 1
 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Jacobsthal sequence gives numbers of zeros and ones in the rows of the tree: A001045(k) = #{i: 2^k <= i < 2^(k+1) and a(i)=0}; A001045(k+1) = #{i: 2^k <= i < 2^(k+1) and a(i)=1}. LINKS N. J. A. Sloane, Stern-Brocot or Farey Tree FORMULA a(1) = 1 and for n>1: a(n) = if A025480(n-1)<>0 and A025480(n)<>0 then a(A025480(n-1)) XOR a(A025480(n)) else if A025480(n)=0 then 1-a(A025480(n-1)) else a(A025480(n-1)). EXAMPLE .[0] . . . . . . . . . . . . . . . . . [1] ................... 1 ........... 1 ............. 0 ....... 1 ..... 0 ..... 1 ..... 1 ..... 1 . 0 . 1 . 1 . 0 . 1 . 1 . 0 .... 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1. CROSSREFS Sequence in context: A065535 A285518 A093719 * A065251 A039982 A267349 Adjacent sequences:  A153775 A153776 A153777 * A153779 A153780 A153781 KEYWORD nonn,tabf AUTHOR Reinhard Zumkeller, Jan 01 2009 STATUS approved

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)