cp's OEIS Frontend

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

%I A301895 #4 Mar 28 2018 15:20:39
%S A301895 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,
%T A301895 16,27,16,27,27,16,16,27,27,16,27,16,16,5,16,27,27,16,27,16,16,5,27,
%U A301895 16,16,5,16,5,5,1,1,32,32,81,32,81,81,64,32,81,81,64,81,64,64,25,32
%N A301895 a(n) = (number of 1's in binary expansion of n)^(number of 0's in binary expansion of n).
%C A301895 Union of A000079 and A000225 without zero gives positions of ones.
%H A301895 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A301895 a(n) = A000120(n)^A023416(n).
%F A301895 a(A000051(n)) = A011782(n).
%e A301895 +---+------+---+---+---------+
%e A301895 | n | bin. |1's|0's|  a(n)   |
%e A301895 +---+------+---+---+---------+
%e A301895 | 0 |    0 | 0 | 1 | 0^1 = 0 |
%e A301895 | 1 |    1 | 1 | 0 | 1^0 = 1 |
%e A301895 | 2 |   10 | 1 | 1 | 1^1 = 1 |
%e A301895 | 3 |   11 | 2 | 0 | 2^0 = 1 |
%e A301895 | 4 |  100 | 1 | 2 | 1^2 = 1 |
%e A301895 | 5 |  101 | 2 | 1 | 2^1 = 2 |
%e A301895 | 6 |  110 | 2 | 1 | 2^1 = 2 |
%e A301895 | 7 |  111 | 3 | 0 | 3^0 = 1 |
%e A301895 | 8 | 1000 | 1 | 3 | 1^3 = 1 |
%e A301895 | 9 | 1001 | 2 | 2 | 2^2 = 4 |
%e A301895 +---+------+---+---+---------+
%e A301895 bin. - n written in base 2;
%e A301895 1's - number of 1's in binary expansion of n;
%e A301895 0's - number of 0's in binary expansion of n.
%t A301895 DigitCount[Range[0, 80], 2, 1]^DigitCount[Range[0, 80], 2, 0]
%Y A301895 Cf. A000051, A000079, A000120, A000225, A011782, A023416, A037861, A070939, A071295, A245788.
%K A301895 nonn,base
%O A301895 0,6
%A A301895 _Ilya Gutkovskiy_, Mar 28 2018