A289831 - OEIS

%I #23 Apr 22 2021 22:03:33

%S 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,

%T 10,11,11,12,13,13,14,15,15,14,15,15,12,13,13,14,15,15,14,15,15,8,9,9,

%U 10,11,11,10,11,11,12,13,13,14,15,15,14,15,15,12

%N a(n) = A289813(n) + A289814(n).

%C 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).

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

%C a(A004488(n)) = a(n).

%H Rémy Sigrist, <a href="/A289831/b289831.txt">Table of n, a(n) for n = 0..6560</a>

%F a(0) = 0.

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

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

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

%e The first values, alongside the ternary representation of n, and the binary representation of a(n), are:

%e n       a(n)    ternary(n)  binary(a(n))

%e --      ----    ----------  ------------

%e 0       0       0           0

%e 1       1       1           1

%e 2       1       2           1

%e 3       2       10          10

%e 4       3       11          11

%e 5       3       12          11

%e 6       2       20          10

%e 7       3       21          11

%e 8       3       22          11

%e 9       4       100         100

%e 10      5       101         101

%e 11      5       102         101

%e 12      6       110         110

%e 13      7       111         111

%e 14      7       112         111

%e 15      6       120         110

%e 16      7       121         111

%e 17      7       122         111

%e 18      4       200         100

%e 19      5       201         101

%e 20      5       202         101

%e 21      6       210         110

%e 22      7       211         111

%e 23      7       212         111

%e 24      6       220         110

%e 25      7       221         111

%e 26      7       222         111

%t Table[FromDigits[Sign@ IntegerDigits[n, 3], 2], {n, 0, 100}] (* _Indranil Ghosh_, Aug 03 2017 *)

%o (PARI) a(n) = my (d=digits(n,3)); fromdigits(vector(#d, i, sign(d[i])), 2)

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o from sympy import sign

%o def a(n):

%o     d=digits(n, 3)[1:]

%o     return int(''.join(str(sign(i)) for i in d), 2)

%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Aug 03 2017

%Y Cf. A000120, A004488, A289813, A289814.

%K nonn,base

%O 0,4

%A _Rémy Sigrist_, Jul 13 2017