

A176893


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


1



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
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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(1d, 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: A213172 A280984 A008810 * A144677 A309677 A058616
Adjacent sequences: A176890 A176891 A176892 * A176894 A176895 A176896


KEYWORD

nonn,easy,base


AUTHOR

Roger L. Bagula, Apr 28 2010


STATUS

approved



