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A179243
Numbers that have three terms in their Zeckendorf representation.
12
12, 17, 19, 20, 25, 27, 28, 30, 31, 32, 38, 40, 41, 43, 44, 45, 48, 49, 50, 52, 59, 61, 62, 64, 65, 66, 69, 70, 71, 73, 77, 78, 79, 81, 84, 93, 95, 96, 98, 99, 100, 103, 104, 105, 107, 111, 112, 113, 115, 118, 124, 125, 126, 128, 131, 136, 148, 150, 151, 153, 154, 155
OFFSET
1,1
LINKS
FORMULA
A007895(a(n)) = 3. - Reinhard Zumkeller, Mar 10 2013
EXAMPLE
12 = 1+3+8;
17 = 1+3+13;
19 = 1+5+13;
20 = 2+5+13;
25 = 21+3+1;
MAPLE
with(combinat): B := proc (n) local A, ct, m, j: A := proc (n) local i: for i while fibonacci(i) <= n do n-fibonacci(i) end do end proc: ct := 0: m := n: for j while 0 < A(m) do ct := ct+1: m := A(m) end do: ct+1 end proc: Q := {}: for i from fibonacci(7)-1 to 160 do if B(i) = 3 then Q := `union`(Q, {i}) else end if end do: Q
MATHEMATICA
zeck = DigitCount[Select[Range[2000], BitAnd[#, 2*#] == 0 &], 2, 1];
Position[zeck, 3] // Flatten (* Jean-François Alcover, Jan 30 2018 *)
PROG
(Haskell)
a179243 n = a179243_list !! (n-1)
a179243_list = filter ((== 3) . a007895) [1..]
-- Reinhard Zumkeller, Mar 10 2013
(Python)
from math import comb, isqrt
from sympy import fibonacci, integer_nthroot
def A179243(n): return fibonacci(2+(r:=n-1-comb((m:=integer_nthroot(6*n, 3)[0])+(t:=(n>comb(m+2, 3)))+1, 3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)), 2))+fibonacci((a:=isqrt(s:=n-comb(m-(t^1)+2, 3)<<1))+((s<<2)>(a<<2)*(a+1)+1)+3)+fibonacci(m+t+5) # Chai Wah Wu, Apr 09 2025
KEYWORD
nonn,look
AUTHOR
Emeric Deutsch, Jul 05 2010
STATUS
approved