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A289831 a(n) = A289813(n) + A289814(n). 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 09:27 EDT 2022. Contains 356005 sequences. (Running on oeis4.)