OFFSET
1,2
REFERENCES
Andrew Ray, On the natural density of the k-Zeckendorf Niven numbers, Ph.D. dissertation, Central Missouri State University, 2005.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Helen G. Grundman, Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.
Andrew Ray and Curtis Cooper, On the natural density of the k-Zeckendorf Niven numbers, J. Inst. Math. Comput. Sci. Math., Vol. 19 (2006), pp. 83-98.
EXAMPLE
12 is in the sequence since A007895(12) = 3 and 3 is a divisor of 12.
MAPLE
fib:= combinat:-fibonacci:
phi:= 1/2 + sqrt(5)/2:
fibapp:= n -> phi^n/sqrt(5):
invfib := proc(x::posint)
local q, n;
q:= evalf((ln(x+1/2) + ln(5)/2)/ln(phi));
n:= floor(q);
if fib(n) <= x then
while fib(n+1) <= x do
n := n+1
end do
else
while fib(n) > x do
n := n-1
end do
end if;
n
end proc:
zeck:= proc(x) local n;
if x = 0 then 0
else
n:= invfib(x);
F[n] + zeck(x-fib(n));
fi
end proc:
filter:= n -> n mod nops(zeck(n)) = 0:
select(filter, [$1..200]); # Robert Israel, Oct 25 2019
MATHEMATICA
z[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; aQ[n_] := Divisible[n, z[n]]; Select[Range[1000], aQ] (* after Alonso del Arte at A007895 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 07 2019
STATUS
approved