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A289814 revision #24

A289814
A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
49
0, 0, 1, 0, 0, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 6, 7, 0, 0, 1, 0, 0, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 6, 7, 8, 8, 9, 8, 8, 9, 10, 10, 11, 8, 8, 9, 8, 8, 9, 10, 10, 11, 12, 12, 13, 12, 12, 13, 14, 14, 15, 0
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
FORMULA
a(0) = 0.
a(3*n) = 2 * a(n).
a(3*n+1) = 2 * a(n).
a(3*n+2) = 2 * a(n) + 1.
Also, a(n) = A289813(A004488(n)).
A053735(n) = A000120(A289813(n)) + 2*A000120(a(n)). - Antti Karttunen, Jul 20 2017
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)
(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 map(a, range(101)) # Indranil Ghosh, Jul 20 2017
CROSSREFS
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Jul 12 2017
STATUS
proposed