|
%I #18 Oct 19 2017 03:14:16
%S 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,
%T 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,
%U 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
%N 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.
%C A003754(n), when written in binary, is the representation of n.
%C Often one uses Fibbinary representations without adjacent ones (the Zeckendorf expansion).
%C a(A000071(n+3)) = n. - _Reinhard Zumkeller_, Aug 10 2014
%D Jay Kappraff, Beyond Measure: A Guided Tour Through Nature, Myth and Number, World Scientific, 2002, page 460.
%H Reinhard Zumkeller, <a href="/A083368/b083368.txt">Table of n, a(n) for n = 1..10000</a>
%F For n = F(a)-1 to F(a+1)-2, a(n) = A035612(F(a+1)-1-n).
%F 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
%e 27 is represented 110111, 28 is 111010; the fourth position changes, so a(28)=4.
%o (Haskell)
%o a083368 n = a083368_list !! (n-1)
%o a083368_list = concat $ h $ drop 2 a000071_list where
%o h (a:fs@(a':_)) = (map (a035612 . (a' -)) [a .. a' - 1]) : h fs
%o -- _Reinhard Zumkeller_, Aug 10 2014
%Y A035612 is the analogous sequence for Zeckendorf representations.
%Y A001511 is the analogous sequence for power-of-two representations.
%Y Cf. A001511, A003714, A003754, A035612.
%Y Cf. A000045, A000071.
%K nonn,base,nice,easy
%O 1,2
%A _Gary W. Adamson_, Jun 04 2003
%E Edited by _Don Reble_, Nov 12 2005
|
