A213064 Bitwise AND of 2n with the one's-complement of n.
0, 2, 4, 4, 8, 10, 8, 8, 16, 18, 20, 20, 16, 18, 16, 16, 32, 34, 36, 36, 40, 42, 40, 40, 32, 34, 36, 36, 32, 34, 32, 32, 64, 66, 68, 68, 72, 74, 72, 72, 80, 82, 84, 84, 80, 82, 80, 80, 64, 66, 68, 68, 72, 74, 72, 72, 64, 66, 68, 68, 64, 66, 64, 64, 128, 130, 132
Offset: 0
Examples
For n = 31, 2n is 62, which in binary is 111110, as multiplication by two is the same as shifting the bits of 31 (11111) to the left by one. As the number is one less than a power of two, all of its least significant bits are set. Before the shift, the most significant bit has a value of 16. After the shift, the most significant bit has a value of 32.
The ~n has all bits set but the five least significant, the highest bit set being the power of two above n: .....111111111100000. When these two values are ANDed together, only the 6th bit, that with the value of 32, is common to them, and the result is 32.
From _Kevin Ryde_, Jun 04 2020: (Start)
n = 1831 = binary 11100100111
a(n) = 2120 = binary 100001001000 1-bit above each run
(End)
Links
Crossrefs
Cf. A048724 (with XOR).
Programs
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C
int a(int n) { return ((n + n) & ~n); } -
Mathematica
Table[BitAnd[2n, -n], {n, 0, 66}] (* Alonso del Arte, Jun 04 2012 *) -
PARI
a(n) = bitnegimply(n<<1,n); \\ Kevin Ryde, Jun 04 2020
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Python
def A213064(n): return n<<1&~n # Chai Wah Wu, Jun 29 2022
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R
# with bitops bitAnd(2 * n, bitFlip(n))
Formula
a(n) = 2n AND ~n
a(n) = 2*A292272(n). - Kevin Ryde, Jun 04 2020
Comments