OFFSET
1,2
COMMENTS
Previous name: Complement of A007417.
Also numbers having infinitary divisor 3, or the same, having factor 3 in their Fermi-Dirac representation as product of distinct terms of A050376. - Vladimir Shevelev, Mar 18 2013
For n > 1: where even terms occur in A051064. - Reinhard Zumkeller, May 23 2013
If we exclude a(1) = 0, these are numbers whose squarefree part is divisible by 3, which can be partitioned into numbers whose squarefree part is congruent to 3 mod 9 (A055041) and 6 mod 9 (A055040) respectively. - Peter Munn, Jul 14 2020
The inclusion of 0 as a term might be viewed as a cultural preference: if we habitually wrote numbers enclosed in brackets and then used a null string of digits for zero, the natural number sequence in ternary would be [], [1], [2], [10], [11], [12], [20], ... . - Peter Munn, Aug 02 2020
The asymptotic density of this sequence is 1/4. - Amiram Eldar, Sep 20 2020
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 42-46.
FORMULA
MAPLE
isA145204 := proc(n) local d, c;
if n = 0 then return true fi;
d := A007089(n); c := 0;
while irem(d, 10) = 0 do c := c+1; d := iquo(d, 10) od;
type(c, odd) end:
select(isA145204, [$(0..231)]); # Peter Luschny, Aug 05 2020
MATHEMATICA
Select[ Range[0, 235], (# // IntegerDigits[#, 3]& // Split // Last // Count[#, 0]& // OddQ)&] (* Jean-François Alcover, Mar 18 2013 *)
Join[{0}, Select[Range[235], OddQ @ IntegerExponent[#, 3] &]] (* Amiram Eldar, Sep 20 2020 *)
PROG
(Haskell)
a145204 n = a145204_list !! (n-1)
a145204_list = 0 : map (+ 1) (findIndices even a051064_list)
-- Reinhard Zumkeller, May 23 2013
(Python)
import numpy as np
def isA145204(n):
if n == 0: return True
c = 0
d = int(np.base_repr(n, base = 3))
while d % 10 == 0:
c += 1
d //= 10
return c % 2 == 1
print([n for n in range(231) if isA145204(n)]) # Peter Luschny, Aug 05 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 04 2008
EXTENSIONS
New name using a comment of Vladimir Shevelev by Peter Luschny, Aug 05 2020
STATUS
approved