

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 bitposition which changes going from n1 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
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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)1n).
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 !! (n1)
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 poweroftwo 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



