|
Search: id:A158705
|
|
|
| A158705 |
|
Nonnegative integers with an odd number of even powers of 2 in their base-2 representation. |
|
+0
3
|
|
| 1, 3, 4, 6, 9, 11, 12, 14, 16, 18, 21, 23, 24, 26, 29, 31, 33, 35, 36, 38, 41, 43, 44, 46, 48, 50, 53, 55, 56, 58, 61, 63, 64, 66, 69, 71, 72, 74, 77, 79, 81, 83, 84, 86, 89, 91, 92, 94, 96, 98
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The nonnegative integers with an even number of even powers of 2 in their base-2 representation are given in A158704.
It appears that a result similar to Prouhet's Theorem holds for the terms of A158704 and A158705, specifically:
Sum[k^j, 0<=k<2^n, k has an even number of even powers of 2]
= Sum[k^j, 0<=k<2^n, k has an odd number of even powers of 2],
for 0<=j<=(n-1)/2. For a recent treatment of this theorem, see the reference.
|
|
REFERENCES
|
Chris Bernhardt, "Evil Twins Alternate with Odious Twins", Math. Mag. 82 (2009) 57-62.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Prouhet-Tarry-EscottProblem
|
|
EXAMPLE
|
The base-2 representation of 6 is 110,i.e. 6=2^2+2^1, with one even power of 2. Thus 6 is a term of the sequence.
|
|
CROSSREFS
|
A000069, A001969, A157971, A158704
Sequence in context: A025061 A037969 A153236 this_sequence A047415 A087805 A153380
Adjacent sequences: A158702 A158703 A158704 this_sequence A158706 A158707 A158708
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
John W. Layman (layman(AT)math.vt.edu), Mar 26 2009
|
|
|
Search completed in 0.002 seconds
|
