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Search: id:A019568
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| A019568 |
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a(n) = smallest k >= 1 such that {1^n, 2^n, 3^n, ..., k^n} can be partitioned into two sets with equal sum; or a(n)=0 if such a partition does not exist. |
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+0
1
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| 2, 3, 7, 12, 16, 24, 31, 39, 47, 44, 60, 71, 79
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) is least integer k such that at least one signed sum of the first k n-th powers equals zero.
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REFERENCES
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Posting to sci.math Nov 11 1996 by fredh(AT)ix.netcom.com (Fred W. Helenius).
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FORMULA
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a(n) == 0 or 3 (mod 4) for n >= 1 - David W. Wilson, Oct 20 2005.
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EXAMPLE
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For n=1 and 2 we have: 1+2-3 = 0 (so a(1)=3), 1+4-9+16-25-36+49 = 0 (so a(2)=7).
The sum of the ninth powers of 3 5 9 10 14 19 20 21 25 26 28 31 35 36 37 38 40 41 42 is half the sum of the ninth powers of 1..44, so a(9)=44 - Don Reble, Oct 21 2005.
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CROSSREFS
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Sequence in context: A046480 A137767 A080140 this_sequence A128458 A066733 A049623
Adjacent sequences: A019565 A019566 A019567 this_sequence A019569 A019570 A019571
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More from Don Reble, Oct 21 2005
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