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%I #13 Jan 23 2017 23:17:21
%S 1,2,1,4,1,6,1,2,1,10,1,4,1,2,1,6,1,6,1,2,1,4,1,4,1,2,1,10,1,6,1,2,1,
%T 4,1,12,1,2,1,8,1,4,1,2,1,6,1,6,1,2,1,4,1,4,1,2,1,6,1,6,1,2,1,4,1,14,
%U 1,2,1,10,1,4,1,2,1,6,1,8,1,2,1,4,1,4,1,2,1,6,1,6,1,2,1,4,1,8,1,2
%N Largest number k such that b - r is even or r = 0 for all b = 1..k where r = n mod b.
%C Consider a text mode screen which is a fixed number of character columns wide. Text only breaks at the screen width, there is no manual line break. Then a(n) is the largest screen width in terms of characters so that a string of n printable characters can be perfectly centrally aligned on this and all smaller widths.
%C a(n) = n for n in {1, 2, 4, 6, 10}, otherwise a(n) < n. The sequence is unbounded.
%H Martin Janecke, <a href="/A281071/b281071.txt">Table of n, a(n) for n = 1..10000</a>
%e a(22) = 4 because
%e 22 mod 1 = 0 where r = 0,
%e 22 mod 2 = 0 where r = 0,
%e 22 mod 3 = 1 where 3 - 1 is even,
%e 22 mod 4 = 2 where 4 - 2 is even, but
%e 22 mod 5 = 2 where r > 0 and 5 - 2 is odd.
%o (PARI) a(n) = {ok = 1; k = 1; while(ok, v = vector(k, b, if ((n % b)==0, 0, b - (n%b))); ok = #select(x->((x % 2)==0), v) == k; if (ok, k++);); k--;} \\ _Michel Marcus_, Jan 23 2017
%Y Cf. A281072.
%K easy,nonn
%O 1,2
%A _Martin Janecke_, Jan 14 2017
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