

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
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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 edgecolored 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

Table of n, a(n) for n=1..41.
G. M. Constantine, Multicolored parallelisms of isomorphic spanning trees, Discrete Mathematics and Theoretical Computer Science, 5(2002), 121126.
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(n2).
G.f.: [x(1+x)(1+x+x^2)]/[12x^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



