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A176893
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a(n) = 2^(number of zeros in binary expansion of n) * 3^(numbers of ones in binary expansion of n).
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1
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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
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0,1
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COMMENTS
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This method doesn't give a distinct encoding of the nonnegative numbers as 54 appears three times and 144 and 216 many more times.
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LINKS
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Table of n, a(n) for n=0..50.
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FORMULA
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a(n) = 2^A023416(n)*3^A000120(n). [R. J. Mathar, Dec 09 2010]
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A000120, A023416.
Sequence in context: A213172 A280984 A008810 * A144677 A309677 A058616
Adjacent sequences: A176890 A176891 A176892 * A176894 A176895 A176896
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KEYWORD
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nonn,easy,base
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AUTHOR
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Roger L. Bagula, Apr 28 2010
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STATUS
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approved
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