

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
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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's0'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



