A176893 a(n) = 2^(number of zeros in binary expansion of n) * 3^(numbers of ones in binary expansion of n).

2, 3, 6, 9, 12, 18, 18, 27, 24, 36, 36, 54, 36, 54, 54, 81, 48, 72, 72, 108, 72, 108, 108, 162, 72, 108, 108, 162, 108, 162, 162, 243, 96, 144, 144, 216, 144, 216, 216, 324, 144, 216, 216, 324, 216, 324, 324, 486, 144, 216, 216

Offset

0,1

Comments

This method doesn't give a distinct encoding of the nonnegative numbers as 54 appears three times and 144 and 216 many more times.

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = 2^A023416(n)*3^A000120(n). [R. J. Mathar, Dec 09 2010]

Maple

A000120 := proc(n) add(d, d=convert(n, base, 2)) ; end proc:
A023416 := proc(n) if n= 0 then 1; else add(1-d, d=convert(n, base, 2)) ; end if; end proc:
A176893 := proc(n) 2^A023416(n)*3^A000120(n); end proc: # R. J. Mathar, Dec 09 2010

Mathematica

Table[2^Count[Table[((IntegerDigits[n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]], 2]*3^Count[Table[(( IntegerDigits[n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]], 3], {n, 1, 51}]
Table[2^DigitCount[n, 2, 0] 3^DigitCount[n, 2, 1], {n, 0, 50}] (* Harvey P. Dale, Oct 29 2012 *)

Crossrefs

Cf. A000120, A023416.

Sequence in context: A008810 A280984 A339485 * A144677 A309677 A058616

Adjacent sequences: A176890 A176891 A176892 * A176894 A176895 A176896

Keyword

nonn,easy,base

Author

Roger L. Bagula, Apr 28 2010

Status

approved