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Template:Sequence of the Day for October 15

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Intended for: October 15, 2011

Timetable

  • First draft entered by Alonso del Arte on August 8, 2011
  • Draft reviewed by Mitch Harris on August 9, 2011
  • Draft approved by Daniel Forgues on October 17, 2012
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



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
2i
.
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.