A035514 - OEIS

A035514

Zeckendorf expansion of n: repeatedly subtract the largest Fibonacci number you can until nothing remains.

0, 1, 2, 3, 31, 5, 51, 52, 8, 81, 82, 83, 831, 13, 131, 132, 133, 1331, 135, 1351, 1352, 21, 211, 212, 213, 2131, 215, 2151, 2152, 218, 2181, 2182, 2183, 21831, 34, 341, 342, 343, 3431, 345, 3451, 3452, 348, 3481, 3482, 3483, 34831, 3413, 34131, 34132

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

REFERENCES

Zeckendorf, E., Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41, 179-182, 1972.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Classic Sequences

EXAMPLE

16 = 13 + 3, so a(16)=13_3 => 133.

PROG

(Haskell)

a035514 n = a035514_list !! (n-1)

a035514_list = map (read . concatMap show) a035516_tabf :: [Integer]

-- Reinhard Zumkeller, Mar 10 2013

CROSSREFS

Cf. A035517, A035515, A035516.