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a(n) = minimum over nonnegative integers m of the size of the largest subset of pairwise relatively prime numbers in {m+1, m+2, ..., m+n}.
2

%I #17 Jun 18 2020 22:55:23

%S 1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,9,

%T 9,9,9,9,9,10,10,10,10,10,10

%N a(n) = minimum over nonnegative integers m of the size of the largest subset of pairwise relatively prime numbers in {m+1, m+2, ..., m+n}.

%H P. Erdős and J. L. Selfridge, <a href="http://www.renyi.hu/~p_erdos/1971-03.pdf">Complete prime subsets of consecutive integers</a>, Proceedings of the Manitoba Conference on Numerical Mathematics, Winnipeg (1971), p. 13.

%e a(5) = 3 because the largest pairwise relatively prime subset of {2,3,4,5,6} is of size 3 (e.g. {2,3,5}) and any 5 consecutive integers must contain at least 3 that are relatively prime

%Y Cf. A062575.

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Jul 03 2001

%E Name corrected by _Wing Hong Tony Wong_, Jun 11 2020