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A219641 a(n) = n minus (number of 1's in Zeckendorf expansion of n). 14
0, 0, 1, 2, 2, 4, 4, 5, 7, 7, 8, 9, 9, 12, 12, 13, 14, 14, 16, 16, 17, 20, 20, 21, 22, 22, 24, 24, 25, 27, 27, 28, 29, 29, 33, 33, 34, 35, 35, 37, 37, 38, 40, 40, 41, 42, 42, 45, 45, 46, 47, 47, 49, 49, 50, 54, 54, 55, 56, 56, 58, 58, 59, 61, 61, 62, 63, 63, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
See A014417 for the Fibonacci number system representation, also known as Zeckendorf expansion.
LINKS
Paul Baird-Smith, Alyssa Epstein, Kristen Flint, and Steven J. Miller, The Zeckendorf Game, arXiv:1809.04881 [math.NT], 2018.
FORMULA
a(n) = n - A007895(n).
MATHEMATICA
zeck = DigitCount[Select[Range[0, 500], BitAnd[#, 2*#] == 0&], 2, 1];
Range[0, Length[zeck]-1] - zeck (* Jean-François Alcover, Jan 25 2018 *)
PROG
(Scheme): (define (A219641 n) (- n (A007895 n)))
(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 str(x).count("1")
print([n - a(n) for n in range(101)]) # Indranil Ghosh, Jun 09 2017
CROSSREFS
Cf. A007895, A014417. A022342 gives the positions of records, resulting the same sequence with duplicates removed: A219640. A035336 gives the positions of values that occur only once: A219639. Cf. also A219637, A219642. Analogous sequence for binary system: A011371, for factorial number system: A219651.
Sequence in context: A337765 A266690 A230421 * A341464 A277758 A240027
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 24 2012
STATUS
approved

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Last modified July 17 09:45 EDT 2024. Contains 374364 sequences. (Running on oeis4.)