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A158705
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Nonnegative integers with an odd number of even powers of 2 in their base-2 representation.
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3
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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REFERENCES
| Chris Bernhardt, "Evil Twins Alternate with Odious Twins", Math. Mag. 82 (2009) 57-62.
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LINKS
| Eric Weisstein's World of Mathematics, Prouhet-Tarry-EscottProblem
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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.
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PROG
| (MAGMA) [ n : n in [0..150] | IsOdd(&+Intseq(n, 4))]; // Vincenzo Librandi, Apr 13 2011
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CROSSREFS
| A000069, A001969, A157971, A158704
Sequence in context: A025061 A037969 A153236 * A047415 A087805 A173318
Adjacent sequences: A158702 A158703 A158704 * A158706 A158707 A158708
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Mar 26 2009
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