OFFSET
0,7
COMMENTS
The ones in the binary representation of a(n) correspond to the twos in the ternary representation of n; for example: ternary(42) = 1120 and binary(a(42)) = 10 (a(42) = 2).
See A289813 for the sequence encoding the ones in ternary representation of n and additional comments.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..6560
FORMULA
EXAMPLE
The first values, alongside the ternary representation of n, and the binary representation of a(n), are:
n a(n) ternary(n) binary(a(n))
-- ---- ---------- ------------
0 0 0 0
1 0 1 0
2 1 2 1
3 0 10 0
4 0 11 0
5 1 12 1
6 2 20 10
7 2 21 10
8 3 22 11
9 0 100 0
10 0 101 0
11 1 102 1
12 0 110 0
13 0 111 0
14 1 112 1
15 2 120 10
16 2 121 10
17 3 122 11
18 4 200 100
19 4 201 100
20 5 202 101
21 4 210 100
22 4 211 100
23 5 212 101
24 6 220 110
25 6 221 110
26 7 222 111
MATHEMATICA
Table[FromDigits[#, 2] &[IntegerDigits[n, 3] /. d_ /; d > 0 :> d - 1], {n, 0, 81}] (* Michael De Vlieger, Jul 20 2017 *)
PROG
(PARI) a(n) = my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2)
(PARI) a(n) = fromdigits(digits(n, 3)\2, 2); \\ Ruud H.G. van Tol, May 08 2024
(Python)
from sympy.ntheory.factor_ import digits
def a(n):
d = digits(n, 3)[1:]
return int("".join('1' if i == 2 else '0' for i in d), 2)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jul 20 2017
CROSSREFS
KEYWORD
AUTHOR
Rémy Sigrist, Jul 12 2017
STATUS
approved