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 A083368 A Fibbinary system represents a number as a sum of distinct Fibonacci numbers (instead of distinct powers of two). Using representations without adjacent zeros, a(n) = the highest bit-position which changes going from n-1 to n. 3
 1, 2, 1, 3, 2, 1, 4, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 7, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 8, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 7, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 9, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A003754(n), when written in binary, is the representation of n. Often one uses Fibbinary representations without adjacent ones (the Zeckendorf expansion). a(A000071(n+3)) = n. - Reinhard Zumkeller, Aug 10 2014 REFERENCES Jay Kappraff, Beyond Measure: A Guided Tour Through Nature, Myth and Number, World Scientific, 2002, page 460. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA For n = F(a)-1 to F(a+1)-2, a(n) = A035612(F(a+1)-1-n). a(n) = a(k)+1 if n = ceiling(phi*k) where phi is the golden ratio; otherwise a(n) = 1. - Tom Edgar, Aug 25 2015 EXAMPLE 27 is represented 110111, 28 is 111010; the fourth position changes, so a(28)=4. PROG (Haskell) a083368 n = a083368_list !! (n-1) a083368_list = concat \$ h \$ drop 2 a000071_list where    h (a:fs@(a':_)) = (map (a035612 . (a' -)) [a .. a' - 1]) : h fs -- Reinhard Zumkeller, Aug 10 2014 CROSSREFS A035612 is the analogous sequence for Zeckendorf representations. A001511 is the analogous sequence for power-of-two representations. Cf. A001511, A003714, A003754, A035612. Cf. A000045, A000071. Sequence in context: A138530 A002341 A128260 * A112379 A246700 A073932 Adjacent sequences:  A083365 A083366 A083367 * A083369 A083370 A083371 KEYWORD nonn,base,nice,easy AUTHOR Gary W. Adamson, Jun 04 2003 EXTENSIONS Edited by Don Reble, Nov 12 2005 STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)