“Star Number”的概念、定义、习题解题方法及翻译-数学辞典

单词

Star Number

释义

Star Number

The number of cells in a generalized Chinese checkers board (or ``centered'' Hexagram).

(1)

The first few are 1, 13, 37, 73, 121, ... (Sloane's A003154). Every star number has Digital Root 1 or 4, and thefinal digits must be one of: 01, 21, 41, 61, 81, 13, 33, 53, 73, 93, or 37.

The first A006060), and canbe computed using

			(2)
			(3)

The first few A006061). Square star numbers are obtained by solving the Diophantine Equation

(4)

and can be computed using

(5)

See also Hex Number, Square Number, Triangular Number

References

Gardner, M. ``Hexes and Stars.'' Ch. 2 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, 1988.

Hindin, H. ``Stars, Hexes, Triangular Numbers, and Pythagorean Triples.'' J. Recr. Math. 16, 191-193, 1983-1984.

Sloane, N. J. A. SequencesA003154/M4893,A006060/M5425, andA006061/M5385in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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