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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 05:39 EDT 2021. Contains 345080 sequences. (Running on oeis4.)