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Search: id:A094958
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| A094958 |
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Numbers of the form 2^n or 5*2^n. |
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+0
8
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| 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 16384, 20480, 32768, 40960, 65536, 81920, 131072, 163840, 262144, 327680, 524288, 655360, 1048576, 1310720, 2097152
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The subset {a(1),...,a(2k)} together with a(2k+2) is the set of proper divisors of 5*2^k.
Comment from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 10 2005: This appears to be the same sequence as "Numbers n such that n^2 is not the sum of three nonzero squares". Don Reble and Paul Pollack respond: Yes, that is correct.
For a(n)>4: number of vertices of complete graphs that can be properly edge-colored in such a way that the edges can be partitioned into edge disjoint multicolored isomorphic spanning trees.
Also numbers k such that k^2=a^2+b^2+c^2 has no solutions in the positive integers a, b and c. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 20 2005
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LINKS
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G. M. Constantine, Multicolored parallelisms of isomorphic spanning trees, Discrete Mathematics and Theoretical Computer Science, 5(2002), 121-126.
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FORMULA
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a(1)=1, a(2)=2, a(3)=4, for n>=0, a(2n+3) = 4*2^n, a(2n+4) = 5*2^n.
Recurrence: for n>4, a(n) = 2a(n-2).
G.f.: [x(1+x)(1+x+x^2)]/[1-2x^2].
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CROSSREFS
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Cf. A029744, A029745. Union of A000079 and A020714.
Complement of A005767.
Sequence in context: A133075 A018433 A115831 this_sequence A018565 A018391 A018310
Adjacent sequences: A094955 A094956 A094957 this_sequence A094959 A094960 A094961
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan, Jun 01 2004
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