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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

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), 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.)