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A214562 Number of 0's in binary expansion of n^n.

%I A214562 #17 Dec 24 2024 12:52:53
%S A214562 0,0,2,1,8,6,10,9,24,15,23,19,34,21,31,26,64,39,49,40,61,44,63,46,95,
%T A214562 59,82,61,98,79,97,71,160,88,112,92,129,96,115,109,160,105,131,118,
%U A214562 178,125,159,134,228,138,178,146,207,141,183,154,245,161,192,167,231,195
%N A214562 Number of 0's in binary expansion of n^n.
%H A214562 Alois P. Heinz, <a href="/A214562/b214562.txt">Table of n, a(n) for n = 0..16383</a>
%F A214562 a(n) = A023416(A000312(n)).
%F A214562 a(2^k) = k*2^k. - _Chai Wah Wu_, Dec 24 2024
%o A214562 (Python)
%o A214562 for n in range(300):
%o A214562    c = 0
%o A214562    b = int(n**n)
%o A214562    while b>0:
%o A214562        c += 1-(b&1)
%o A214562        b//=2
%o A214562    print( c, end=", ")
%o A214562 (PARI) vector(66, n, b=binary((n-1)^(n-1)); sum(j=1, #b, 1-b[j])) /* _Joerg Arndt_, Jul 21 2012 */
%Y A214562 Cf. A023416, A078565, A214560.
%K A214562 nonn,base
%O A214562 0,3
%A A214562 _Alex Ratushnyak_, Jul 21 2012