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Search: id:A158704
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| A158704 |
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Nonnegative integers with an even number of even powers of 2 in their base-2 representation. |
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+0
2
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| 0, 2, 5, 7, 8, 10, 13, 15, 17, 19, 20, 22, 25, 27, 28, 30, 32, 34, 37, 39, 40, 42, 45, 47, 49, 51, 52, 54, 57, 59, 60, 62, 65, 67, 68, 70, 73, 75, 76, 78, 80, 82, 85, 87, 88, 90, 93, 95, 97, 99, 100
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The nonnegative integers with an odd number of even powers of 2 in their base-2 representation are given in A158705.
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-1, k has an even number of even powers of 2] = Sum[k^j, 0<=k<2^n-1, 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.
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REFERENCES
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Chris Bernhardt, "Evil Twins Alternate with Odious Twins", Math. Mag. 82 (2009) 57-62.
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LINKS
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Eric Weisstein's World of Mathematics, Prouhet-Tarry-EscottProblem
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EXAMPLE
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The base-2 representation of 5 is 101,i.e. 5=2^2+2^0, with two even powers of 2. Thus 5 is a term of the sequence.
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CROSSREFS
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A000069, A001969, A157971, A158705
Sequence in context: A034028 A102700 A047481 this_sequence A131854 A005124 A160530
Adjacent sequences: A158701 A158702 A158703 this_sequence A158705 A158706 A158707
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Mar 24 2009
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