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

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, 59, 82, 61, 98, 79, 97, 71, 160, 88, 112, 92, 129, 96, 115, 109, 160, 105, 131, 118, 178, 125, 159, 134, 228, 138, 178, 146, 207, 141, 183, 154, 245, 161, 192, 167, 231, 195

Offset: 0

Author

Alex Ratushnyak, Jul 21 2012

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16383

Crossrefs

Cf. A023416, A078565, A214560.

Programs

PARI

vector(66, n, b=binary((n-1)^(n-1)); sum(j=1, #b, 1-b[j])) /* Joerg Arndt, Jul 21 2012 */

Python

for n in range(300):
   c = 0
   b = int(n**n)
   while b>0:
       c += 1-(b&1)
       b//=2
   print( c, end=", ")

Formula

a(n) = A023416(A000312(n)).

a(2^k) = k*2^k. - Chai Wah Wu, Dec 24 2024