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A095098 Fib001 numbers: those k for which the Zeckendorf expansion A014417(k) ends with two zeros and a final one.

%I A095098 #29 Mar 21 2022 08:07:52
%S A095098 6,9,14,19,22,27,30,35,40,43,48,53,56,61,64,69,74,77,82,85,90,95,98,
%T A095098 103,108,111,116,119,124,129,132,137,142,145,150,153,158,163,166,171,
%U A095098 174,179,184,187,192,197,200,205,208,213,218,221,226,229,234,239,242
%N A095098 Fib001 numbers: those k for which the Zeckendorf expansion A014417(k) ends with two zeros and a final one.
%C A095098 The asymptotic density of this sequence is sqrt(5)-2. - _Amiram Eldar_, Mar 21 2022
%H A095098 Amiram Eldar, <a href="/A095098/b095098.txt">Table of n, a(n) for n = 1..10000</a>
%F A095098 a(n) = 2*floor((n+1)*phi^2)-n-3, where phi = (1+sqrt(5))/2. - _Vladeta Jovovic_, Jul 05 2004
%t A095098 a[n_] = 2 Floor[(n + 1) GoldenRatio^2] - n - 3;
%t A095098 a /@ Range[100] (* _Jean-François Alcover_, Oct 28 2019, after _Vladeta Jovovic_ *)
%o A095098 (Python)
%o A095098 from sympy import fibonacci
%o A095098 def a(n):
%o A095098     k=0
%o A095098     x=0
%o A095098     while n>0:
%o A095098         k=0
%o A095098         while fibonacci(k)<=n: k+=1
%o A095098         x+=10**(k - 3)
%o A095098         n-=fibonacci(k - 1)
%o A095098     return x
%o A095098 def ok(n): return str(a(n))[-3:]=="001"
%o A095098 print([n for n in range(1, 501) if ok(n)]) # _Indranil Ghosh_, Jun 08 2017
%Y A095098 Cf. A014417, A095086 (fib001 primes).
%Y A095098 Set-wise difference of A003622 - A134860.
%K A095098 nonn,base
%O A095098 1,1
%A A095098 _Antti Karttunen_, Jun 01 2004