

A112309


Triangle read by rows: row n gives terms in lazy Fibonacci representation of n.


3



1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 5, 1, 2, 5, 1, 3, 5, 2, 3, 5, 1, 2, 3, 5, 1, 3, 8, 2, 3, 8, 1, 2, 3, 8, 2, 5, 8, 1, 2, 5, 8, 1, 3, 5, 8, 2, 3, 5, 8, 1, 2, 3, 5, 8, 2, 5, 13, 1, 2, 5, 13, 1, 3, 5, 13, 2, 3, 5, 13, 1, 2, 3, 5, 13, 1, 3, 8, 13, 2, 3, 8, 13, 1, 2, 3, 8, 13, 2, 5, 8, 13, 1, 2, 5, 8, 13, 1, 3
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OFFSET

1,2


COMMENTS

Write n as a sum c_2 F_2 + c_3 F_3 + ..., where the F_i are Fibonacci numbers and the c_i are 0 or 1. The lazy expansion is the minimal one in the lexicographic order, in contrast to the Zeckendorf expansion (A035517, A007895), which is the maximal one.
In other words we give preference to the smallest Fibonacci numbers.


LINKS

Table of n, a(n) for n=1..100.
W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, Fib. Q., 43 (No. 1, 2005), 6069.


EXAMPLE

Triangle begins:
1 meaning 1 = 1
2 meaning 2 = 2
1 2 meaning 3 = 1+2
1 3 meaning 4 = 1+3
2 3 meaning 5 = 2+3
1 2 3 meaning 6 = 1+2+3 (and not the Zeckendorf expansion 1+5)
2 5 meaning 7 = 2+5


MATHEMATICA

DeleteCases[IntegerDigits[Range[200], 2], {___, 0, 0, ___}]
A112309 = Map[DeleteCases[Reverse[#] Fibonacci[Range[Length[#]] + 1], 0] &, DeleteCases[IntegerDigits[1 + Range[200], 2], {___, 0, 0, ___}]]
A112310 = Map[Length, A112309]
(* Peter J. C. Moses, Mar 03 2015 *)


CROSSREFS

Cf. A000045, A112310, A035517, A007895.
Sequence in context: A259177 A304036 A173442 * A160006 A060682 A280363
Adjacent sequences: A112306 A112307 A112308 * A112310 A112311 A112312


KEYWORD

nonn,tabf,easy


AUTHOR

N. J. A. Sloane, Dec 01 2005


EXTENSIONS

Extended by Ray Chandler, Dec 01 2005


STATUS

approved



