Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A093509
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A093509 Multiples of 5 or 6. +0
1
0, 5, 6, 10, 12, 15, 18, 20, 24, 25, 30, 35, 36, 40, 42, 45, 48, 50, 54, 55, 60, 65, 66, 70, 72, 75, 78, 80, 84, 85, 90, 95, 96, 100, 102, 105, 108, 110, 114, 115, 120, 125, 126, 130, 132, 135, 138, 140, 144, 145, 150, 155, 156, 160, 162, 165, 168, 170, 174, 175 (list; graph; listen)
OFFSET

1,2

COMMENT

Numbers that are congruent to {0, 5, 6, 10, 12, 15, 18, 20, 24, 25} mod 30.

Also without 0: numbers n such that cos(Pi*x/n)+cos(Pi*y/n)=1/2 has integer solutions (x,y).

Numbers n such that there exists a nontrivial configuration to an n-1 x n-1 Lights Out game from the all-off state to the all-off state.

REFERENCES

J. H. Conway and A. D. Jones, Trigonometric Diophantine equations (on vanishing sums of roots of unity), Acta Arith. XXX (1976) 229-240.

LINKS

M. Hunziker, A. Machiavelo and J. Park, Chebyshev polynomials over finite fields and reversibility of s-automata...

Eric Weisstein's World of Mathematics, Lights Out Puzzle

FORMULA

G.f.: x^2*(5-4*x+8*x^2-6*x^3+9*x^4-6*x^5+8*x^6-4*x^7+5*x^8) / ((x^4+x^3+x^2+x+1) * ( x^4-x^3+x^2-x+1) * (x-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

EXAMPLE

102 = 6*17, so 102 is in sequence.

CROSSREFS

Sequence in context: A037359 A099538 A093614 this_sequence A105953 A164095 A102506

Adjacent sequences: A093506 A093507 A093508 this_sequence A093510 A093511 A093512

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan (ralf(AT)ark.in-berlin.de), May 22 2004

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 29 12:46 EST 2009. Contains 167659 sequences.


AT&T Labs Research