Zeckendorf table

Table of numbers used by Tony Padilla in Numberphile video from Jan 9, 2026:
https://www.youtube.com/watch?v=S5FTe5KP2Cw
List of Fibonacci numbers less than 100. Exclude the initial 1.
In[]:=
fibs=Select[Map[Fibonacci,Range[2,15]],#<100&]
Out[]=
{1,2,3,5,8,13,21,34,55,89}
Reversed Zeckendorf representation of each number from 1 through 100. Reversing puts the least significant Fibonacci term first.
In[]:=
rzeck=Map[Reverse,Map[ResourceFunction["ZeckendorfRepresentation"],Range[1,100]]];
An example from rzeck and the list of associated Fibonacci numbers.
In[]:=
rzeck[[50]]
Out[]=
{0,0,1,0,0,1,0,1}
In[]:=
fibs[[Flatten[Position[rzeck[[50]],1]]]]
Out[]=
{3,13,34}
Build a list of the Fibonacci terms for each number from 1 through 100
In[]:=
fibTerms[n_]:=fibs[[Flatten[Position[rzeck[[n]],1]]]]
In[]:=
f=Map[fibTerms,Range[1,100]]
Out[]=
{{1},{2},{3},{1,3},{5},{1,5},{2,5},{8},{1,8},{2,8},{3,8},{1,3,8},{13},{1,13},{2,13},{3,13},{1,3,13},{5,13},{1,5,13},{2,5,13},{21},{1,21},{2,21},{3,21},{1,3,21},{5,21},{1,5,21},{2,5,21},{8,21},{1,8,21},{2,8,21},{3,8,21},{1,3,8,21},{34},{1,34},{2,34},{3,34},{1,3,34},{5,34},{1,5,34},{2,5,34},{8,34},{1,8,34},{2,8,34},{3,8,34},{1,3,8,34},{13,34},{1,13,34},{2,13,34},{3,13,34},{1,3,13,34},{5,13,34},{1,5,13,34},{2,5,13,34},{55},{1,55},{2,55},{3,55},{1,3,55},{5,55},{1,5,55},{2,5,55},{8,55},{1,8,55},{2,8,55},{3,8,55},{1,3,8,55},{13,55},{1,13,55},{2,13,55},{3,13,55},{1,3,13,55},{5,13,55},{1,5,13,55},{2,5,13,55},{21,55},{1,21,55},{2,21,55},{3,21,55},{1,3,21,55},{5,21,55},{1,5,21,55},{2,5,21,55},{8,21,55},{1,8,21,55},{2,8,21,55},{3,8,21,55},{1,3,8,21,55},{89},{1,89},{2,89},{3,89},{1,3,89},{5,89},{1,5,89},{2,5,89},{8,89},{1,8,89},{2,8,89},{3,8,89}}
“Invert” list f by selecting the numbers that include each Fibonacci number in their Zeckendorf representation. This is the table in the video.
In[]:=
Table[Select[f,MemberQ[i]->Index],{i,fibs}]
Out[]=
{{1,4,6,9,12,14,17,19,22,25,27,30,33,35,38,40,43,46,48,51,53,56,59,61,64,67,69,72,74,77,80,82,85,88,90,93,95,98},{2,7,10,15,20,23,28,31,36,41,44,49,54,57,62,65,70,75,78,83,86,91,96,99},{3,4,11,12,16,17,24,25,32,33,37,38,45,46,50,51,58,59,66,67,71,72,79,80,87,88,92,93,100},{5,6,7,18,19,20,26,27,28,39,40,41,52,53,54,60,61,62,73,74,75,81,82,83,94,95,96},{8,9,10,11,12,29,30,31,32,33,42,43,44,45,46,63,64,65,66,67,84,85,86,87,88,97,98,99,100},{13,14,15,16,17,18,19,20,47,48,49,50,51,52,53,54,68,69,70,71,72,73,74,75},{21,22,23,24,25,26,27,28,29,30,31,32,33,76,77,78,79,80,81,82,83,84,85,86,87,88},{34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54},{55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88},{89,90,91,92,93,94,95,96,97,98,99,100}}