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

0,6

Comments

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

Links

Table of n, a(n) for n=0..80.

Index entries for sequences related to binary expansion of n

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]

Crossrefs

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

Sequence in context: A108017 A293208 A247364 * A229054 A133135 A292189

Adjacent sequences: A301892 A301893 A301894 * A301896 A301897 A301898

Keyword

nonn,base

Author

Ilya Gutkovskiy, Mar 28 2018

Status

approved