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

6, 9, 14, 19, 22, 27, 30, 35, 40, 43, 48, 53, 56, 61, 64, 69, 74, 77, 82, 85, 90, 95, 98, 103, 108, 111, 116, 119, 124, 129, 132, 137, 142, 145, 150, 153, 158, 163, 166, 171, 174, 179, 184, 187, 192, 197, 200, 205, 208, 213, 218, 221, 226, 229, 234, 239, 242

Offset

1,1

Comments

The asymptotic density of this sequence is sqrt(5)-2. - Amiram Eldar, Mar 21 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2*floor((n+1)*phi^2)-n-3, where phi = (1+sqrt(5))/2. - Vladeta Jovovic, Jul 05 2004

Mathematica

a[n_] = 2 Floor[(n + 1) GoldenRatio^2] - n - 3;
a /@ Range[100] (* Jean-François Alcover, Oct 28 2019, after Vladeta Jovovic *)

Prog

(Python)
from sympy import fibonacci
def a(n):
    k=0
    x=0
    while n>0:
        k=0
        while fibonacci(k)<=n: k+=1
        x+=10**(k - 3)
        n-=fibonacci(k - 1)
    return x
def ok(n): return str(a(n))[-3:]=="001"
print([n for n in range(1, 501) if ok(n)]) # Indranil Ghosh, Jun 08 2017

Crossrefs

Cf. A014417, A095086 (fib001 primes).

Set-wise difference of A003622 - A134860.

Sequence in context: A129413 A315986 A190461 * A134859 A315987 A315988

Adjacent sequences: A095095 A095096 A095097 * A095099 A095100 A095101

Keyword

nonn,base

Author

Antti Karttunen, Jun 01 2004

Status

approved