

A080804


Least number of connected subgraphs of the binary cube GF(2)^n such that every vertex of GF(2)^n lies in at least one of the subgraphs and no two vertices lie in the same set of subgraphs (such a collection is called an identifying set).


7



1, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78
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OFFSET

1,2


COMMENTS

a(n1) is also the minimum number of matches in a tournament to fairly determine the best two players from n >= 2 contestants. For example, a(81) = a(7) = 9 matches are required to determine the best two players from 8 participants. See Steinhaus (1983).  Hugo Pfoertner, Dec 13 2022


REFERENCES

Hugo Steinhaus, Mathematical Snapshots, Third American Edition, Oxford University Press, New York, 1983, pp 5455.


LINKS



FORMULA

a(n) = n + floor(log_2(n)).


MATHEMATICA



CROSSREFS



KEYWORD

easy,nonn


AUTHOR

Pete Rosendahl (perosen(AT)utu.fi), Mar 26 2003


EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003


STATUS

approved



