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A298306
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The Frobenius number of the set of binary n-th powers, divided out by its GCD.
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0
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OFFSET
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2,1
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COMMENTS
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The binary n-th powers are those positive integers whose base-2 representation consists of n consecutive identical blocks. For example, the binary squares 3, 10, 15, ... form sequence A020330. The GCD of the binary n-th powers form sequence A014491. The Frobenius number of a set S with GCD 1 is the largest number not representable as an N-linear combination of members of S.
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LINKS
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Table of n, a(n) for n=2..6.
Daniel M. Kane, Carlo Sanna, and Jeffrey Shallit, Waring's theorem for binary powers, arXiv:1801.04483 [math.NT], Jan 13 2018.
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EXAMPLE
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For n = 2 the first few binary squares are 3, 10, 15, 36, ... with GCD 1 and the Frobenius number of (3, 10, 15, 36) is 17.
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CROSSREFS
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Cf. A020330, A014491.
Sequence in context: A012193 A128274 A012085 * A308696 A308594 A308570
Adjacent sequences: A298303 A298304 A298305 * A298307 A298308 A298309
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KEYWORD
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nonn,more
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AUTHOR
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Jeffrey Shallit, Jan 16 2018
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STATUS
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approved
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