

A256133


Numbers n that have unique expansion with minimal digit sum in terms of Fibonacci numbers F_k (k > 1).


2



1, 2, 3, 5, 7, 8, 9, 11, 13, 14, 15, 18, 20, 21, 22, 23, 24, 29, 30, 32, 34, 35, 36, 37, 39, 41, 47, 48, 49, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 76, 77, 78, 79, 84, 85, 87, 89, 90, 91, 92, 94, 96, 97, 98, 100, 102, 103, 104, 107, 109, 123, 124, 125, 126
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OFFSET

1,2


COMMENTS

This sequence shows that the "proper digital expansion" mentioned in the introduction to the paper by Drmota and Gajdosik (see Links) is not unique.
This sequence consists of all positive integers that have Zeckendorf expansions not containing any ...1001... and not ending in ...101. Example: 20 is in and it has 20 = 13 + 5 + 2 with Zeckendorf expansion 101010, while 19 is not in and has 19 = 13 + 5 + 1 with Zeckendorf expansion 101001.  Thomas Bier, Oct 09 2015


LINKS

Patrick Okolo Edeogu, Table of n, a(n) for n = 1..141
M. Drmota and M. Gajdosik, The parity of the sum of digits function of generalized Zeckendorf expansions, The Fibonacci Quarterly, 36:1 (1988), pp. 319.


EXAMPLE

7 = 5 + 2 is unique with respect to its minimal digit sum 1 + 1 = 2.
But 10 = 8 + 2 = 5 + 5 is not unique with respect to its minimal digit sum 1 + 1 = 2.


MAPLE

x0:=0: x1:=1: ML:=[]: L:=[]: mes:=0: for r from 2 to 14 do: z:=x1+x0: x0:=x1: x1:=z: rj:=12: L:=[op(L), z]: ML:=[z, op(ML)]: od: XL:=[]: for m from 1 to 400 do: NL:=[]: n:=m: for j from 12 to 1 by 1 do: if L[j+1]>n and L[j]1 < n then NL:=[op(NL), j]: n:=nL[j]: fi: od: eps:=0: nx:=nops(NL): for j from 1 to nx1 do: if NL[j]NL[j+1]=3 then eps:=1: fi: if NL[nx1]NL[nx]=2 and NL[nx]=1 then eps:=1: fi:od: if eps=0 then XL:=[op(XL), m]: fi: od: print(XL);


CROSSREFS

Cf. A000045.
Sequence in context: A039019 A047255 A062062 * A078643 A137698 A063743
Adjacent sequences: A256130 A256131 A256132 * A256134 A256135 A256136


KEYWORD

nonn


AUTHOR

Patrick Okolo Edeogu, Jul 10 2015


STATUS

approved



