Re: fibint(n), fibbinary(n)

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2026-01-11 18:18, Bill Allombert wrote:
> On Sun, Jan 11, 2026 at 05:45:42PM +0100, Ruud H.G. van Tol wrote:

>> I'm looking for an effective (discrete, loop-less) way to derive the 
n-th
>> fibbinary number (Zeckendorf representation).
>> For definitions, see https://oeis.org/A003714.
>>
>> [ n | n<-[0..100], !bitand(n,n>>1) ]
>> [0,
>> 1,
>> 2,
>> 4, 5,
>> 8, 9, 10,
>> 16, 17, 18, 20, 21,
>> 32, 33, 34, 36, 37, 40, 41, 42,
>> 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85
>> ]
>>
>> - - - - - -
>>
>> While on that path, I'm currently also looking for a discrete 
implementation
>> of "fibint", and rather without loop.
>> I think that fibint(n) should return the index of the fibonacci 
number <= n.
>
> fibintexa(n)=round(log(sqrt(5)*n)/log((1+sqrt(5))/2))
> fibint(n)=my(m=fibintexa(n),f=fibonacci(m));if(f>n,f-1,f);

Thanks Bill. You obviously meant

fibint(n)= my(m=fibintexa(n)); if(fibonacci(m)>n,m-1,m);

which indeed performs good.


I then also made that:
fibintexa1(n)= my(sqrt_5=2*quadgen(5)-1); 
round(log(sqrt_5*n)/log((1+sqrt_5)/2));
fibint1(n)= my(m=fibintexa1(n)); if(fibonacci(m)>n,m-1,m);

but my goal is to avoid floating point usage, so I'm still walking. :)

-- Ruud