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 A094958 Numbers of the form 2^n or 5*2^n. 13
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The subset {a(1),...,a(2k)} together with a(2k+2) is the set of proper divisors of 5*2^k. 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. (Editor's note: The following 3 comments are equivalent.) From Wouter Meeussen, 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. 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, Apr 20 2005 The only natural numbers which cannot be the lengths of an interior diagonal of a cuboid with natural edges. - Michael Somos, Mar 02 2004 REFERENCES W. Sierpinski, Pythagorean triangles, Dover Publications, Inc., Mineola, NY, 2003, p. 101 MR2002669 LINKS G. M. Constantine, Multicolored parallelisms of isomorphic spanning trees, Discrete Mathematics and Theoretical Computer Science, 5(2002), 121-126. Index entries for linear recurrences with constant coefficients, signature (0,2) FORMULA 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]. MATHEMATICA With[{c=2^Range[0, 30]}, Union[Join[c, 5c]]] (* Harvey P. Dale, Jul 15 2012 *) CROSSREFS Cf. A029744, A029745. Union of A000079 and A020714. Complement of A005767. Sequence in context: A018433 A228939 A115831 * A018565 A018391 A018310 Adjacent sequences:  A094955 A094956 A094957 * A094959 A094960 A094961 KEYWORD nonn,easy AUTHOR Ralf Stephan, Jun 01 2004 EXTENSIONS Edited by T. D. Noe and M. F. Hasler, Nov 12 2010 STATUS approved

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Last modified October 15 18:18 EDT 2019. Contains 328037 sequences. (Running on oeis4.)