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a(n) is the largest m such that n is congruent to -2, -1, 0, 1 or 2 mod k for all k from 1 to m.
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%I #9 Jan 12 2013 21:28:52

%S 5,6,7,8,9,10,5,6,6,7,7,8,5,9,6,6,7,7,5,8,8,6,6,9,5,7,7,8,6,6,5,9,7,7,

%T 7,6,5,8,8,8,7,7,5,6,9,8,8,8,5,6,6,9,9,9,5,8,6,6,7,10,5,9,9,6,6,7,5,

%U 10,10,10,6,6,5,7,7,8,11,6,5,10,7,7,7,8,5

%N a(n) is the largest m such that n is congruent to -2, -1, 0, 1 or 2 mod k for all k from 1 to m.

%t f[n_] := Block[{k = 4, r}, While[r = Mod[n, k]; r < 3 || k - r < 3, k++]; k - 1]; Array[f, 100, 3]

%Y Cf. A187824.

%K easy,nonn

%O 3,1

%A _Robert G. Wilson v_, Jan 09 2013