A301895 a(n) = (number of 1's in binary expansion of n)^(number of 0's in binary expansion of n).

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

Author

Ilya Gutkovskiy, Mar 28 2018

Keywords

• nonn
• base

Comments

Union of A000079 and A000225 without zero gives positions of ones.

Examples

			+---+------+---+---+---------+
| 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.
		

Links

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000051, A000079, A000120, A000225, A011782, A023416, A037861, A070939, A071295, A245788.

Programs

Mathematica

DigitCount[Range[0, 80], 2, 1]^DigitCount[Range[0, 80], 2, 0]

Formula

a(n) = A000120(n)^A023416(n).

a(A000051(n)) = A011782(n).