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Fib001 numbers: those k for which the Zeckendorf expansion A014417(k) ends with two zeros and a final one.
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%I #29 Mar 21 2022 08:07:52

%S 6,9,14,19,22,27,30,35,40,43,48,53,56,61,64,69,74,77,82,85,90,95,98,

%T 103,108,111,116,119,124,129,132,137,142,145,150,153,158,163,166,171,

%U 174,179,184,187,192,197,200,205,208,213,218,221,226,229,234,239,242

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

%C The asymptotic density of this sequence is sqrt(5)-2. - _Amiram Eldar_, Mar 21 2022

%H Amiram Eldar, <a href="/A095098/b095098.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2*floor((n+1)*phi^2)-n-3, where phi = (1+sqrt(5))/2. - _Vladeta Jovovic_, Jul 05 2004

%t a[n_] = 2 Floor[(n + 1) GoldenRatio^2] - n - 3;

%t a /@ Range[100] (* _Jean-François Alcover_, Oct 28 2019, after _Vladeta Jovovic_ *)

%o (Python)

%o from sympy import fibonacci

%o def a(n):

%o k=0

%o x=0

%o while n>0:

%o k=0

%o while fibonacci(k)<=n: k+=1

%o x+=10**(k - 3)

%o n-=fibonacci(k - 1)

%o return x

%o def ok(n): return str(a(n))[-3:]=="001"

%o print([n for n in range(1, 501) if ok(n)]) # _Indranil Ghosh_, Jun 08 2017

%Y Cf. A014417, A095086 (fib001 primes).

%Y Set-wise difference of A003622 - A134860.

%K nonn,base

%O 1,1

%A _Antti Karttunen_, Jun 01 2004