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A301895
a(n) = (number of 1's in binary expansion of n)^(number of 0's in binary expansion of n).
0
0, 1, 1, 1, 1, 2, 2, 1, 1, 4, 4, 3, 4, 3, 3, 1, 1, 8, 8, 9, 8, 9, 9, 4, 8, 9, 9, 4, 9, 4, 4, 1, 1, 16, 16, 27, 16, 27, 27, 16, 16, 27, 27, 16, 27, 16, 16, 5, 16, 27, 27, 16, 27, 16, 16, 5, 27, 16, 16, 5, 16, 5, 5, 1, 1, 32, 32, 81, 32, 81, 81, 64, 32, 81, 81, 64, 81, 64, 64, 25, 32
OFFSET
0,6
COMMENTS
Union of A000079 and A000225 without zero gives positions of ones.
FORMULA
a(n) = A000120(n)^A023416(n).
a(A000051(n)) = A011782(n).
EXAMPLE
+---+------+---+---+---------+
| n | bin. |1's|0's| a(n) |
+---+------+---+---+---------+
| 0 | 0 | 0 | 1 | 0^1 = 0 |
| 1 | 1 | 1 | 0 | 1^0 = 1 |
| 2 | 10 | 1 | 1 | 1^1 = 1 |
| 3 | 11 | 2 | 0 | 2^0 = 1 |
| 4 | 100 | 1 | 2 | 1^2 = 1 |
| 5 | 101 | 2 | 1 | 2^1 = 2 |
| 6 | 110 | 2 | 1 | 2^1 = 2 |
| 7 | 111 | 3 | 0 | 3^0 = 1 |
| 8 | 1000 | 1 | 3 | 1^3 = 1 |
| 9 | 1001 | 2 | 2 | 2^2 = 4 |
+---+------+---+---+---------+
bin. - n written in base 2;
1's - number of 1's in binary expansion of n;
0's - number of 0's in binary expansion of n.
MATHEMATICA
DigitCount[Range[0, 80], 2, 1]^DigitCount[Range[0, 80], 2, 0]
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Mar 28 2018
STATUS
approved