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 A098457 Farey Bisection Expansion of sqrt(7). 2
 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We define the Farey Bisection Expansion (FBE) of the nonnegative real number x to be the sequence {a(n)} of 0's and 1's determined as follows. Set na(0)=0, da(0)=1, nb(0)=1 and db(0)=0. For n=1, 2, 3,..., set num=na(n-1)+nb(n-1) and den=da(n-1)+db(n-1); if x7. a(n) = 1 - Sum_{k=1..4} floor((n + k)/7)*(-1)^k. (End) a(n+1) = (-1)^(mod(mod(n, 7), 3)>0) * A131372(n). - Michael Somos, Dec 26 2016 EXAMPLE G.f. = x + x^2 + x^4 + x^6 + x^7 + x^8 + x^9 + x^11 + x^13 + x^14 + x^15 + ... MAPLE seq(op([1, 1, 0, 1, 0, 1, 1]), n=0..20); # Wesley Ivan Hurt, Jul 11 2016 MATHEMATICA LinearRecurrence[{0, 0, 0, 0, 0, 0, 1}, {1, 1, 0, 1, 0, 1, 1}, 105] (* Ray Chandler, Aug 26 2015 *) PROG (Magma) &cat [[1, 1, 0, 1, 0, 1, 1]^^20]; // Wesley Ivan Hurt, Jul 11 2016 (PARI) {a(n) = [1, 1, 0, 1, 0, 1, 1][(n-1)%7+1]}; /* Michael Somos, Dec 26 2016 */ CROSSREFS Cf. A010121, A097853, A098458, A131372. Sequence in context: A267579 A285414 A131372 * A284793 A260397 A137161 Adjacent sequences: A098454 A098455 A098456 * A098458 A098459 A098460 KEYWORD nonn,easy AUTHOR John W. Layman, Sep 08 2004 STATUS approved

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Last modified September 18 03:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)