A289831 a(n) = A289813(n) + A289814(n).

0, 1, 1, 2, 3, 3, 2, 3, 3, 4, 5, 5, 6, 7, 7, 6, 7, 7, 4, 5, 5, 6, 7, 7, 6, 7, 7, 8, 9, 9, 10, 11, 11, 10, 11, 11, 12, 13, 13, 14, 15, 15, 14, 15, 15, 12, 13, 13, 14, 15, 15, 14, 15, 15, 8, 9, 9, 10, 11, 11, 10, 11, 11, 12, 13, 13, 14, 15, 15, 14, 15, 15, 12

Offset

0,4

Comments

The ones in the binary representation of a(n) correspond to the nonzero digits in the ternary representation of n; for example: ternary(42) = 1120 and binary(a(42)) = 1110 (a(42) = 14).

Each number k >= 0 appears 2^A000120(k) times.

a(A004488(n)) = a(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Formula

a(0) = 0.

a(3*n) = 2*a(n).

a(3*n + 1) = 2*a(n) + 1.

a(3*n + 2) = 2*a(n) + 1.

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       1       1           1
2       1       2           1
3       2       10          10
4       3       11          11
5       3       12          11
6       2       20          10
7       3       21          11
8       3       22          11
9       4       100         100
10      5       101         101
11      5       102         101
12      6       110         110
13      7       111         111
14      7       112         111
15      6       120         110
16      7       121         111
17      7       122         111
18      4       200         100
19      5       201         101
20      5       202         101
21      6       210         110
22      7       211         111
23      7       212         111
24      6       220         110
25      7       221         111
26      7       222         111

Mathematica

Table[FromDigits[Sign@ IntegerDigits[n, 3], 2], {n, 0, 100}] (* Indranil Ghosh, Aug 03 2017 *)

Prog

(PARI) a(n) = my (d=digits(n, 3)); fromdigits(vector(#d, i, sign(d[i])), 2)
(Python)
from sympy.ntheory.factor_ import digits
from sympy import sign
def a(n):
    d=digits(n, 3)[1:]
    return int(''.join(str(sign(i)) for i in d), 2)
print([a(n) for n in range(101)]) # Indranil Ghosh, Aug 03 2017

Crossrefs

Cf. A000120, A004488, A289813, A289814.

Sequence in context: A238756 A025076 A110006 * A335358 A296611 A308661

Adjacent sequences: A289828 A289829 A289830 * A289832 A289833 A289834

Keyword

nonn,base

Author

Rémy Sigrist, Jul 13 2017

Status

approved