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# OeisWiki:Community Portal

## Contents

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## Sequence of the Day for October 15

A011371:
 n
minus its binary weight,
 n   ≥   0
.
{ 0, 0, 1, 1, 3, 3, 4, 4, 7, 7, ... }
This is also the exponent of the highest power of 2 dividing
 n!
 ⌊  log2(n) ⌋ ∑ i   = 1

 n 2 i
.
This sequence shows why, in binary, 0 and 1 are the only two numbers
 n
such that
 n
equals the sum of its digits raised to the consecutive powers. 1 raised to any consecutive power is still 1 and thus any sum of digits raised to consecutive powers for any
 n > 1
falls short of equaling the value of
 n
by the
 n
-th number of this sequence.