A281071 Largest number k such that b - r is even or r = 0 for all b = 1..k where r = n mod b.

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, 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, 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

Offset: 1

Author

Martin Janecke, Jan 14 2017

Keywords

• easy
• nonn

Comments

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.

a(n) = n for n in {1, 2, 4, 6, 10}, otherwise a(n) < n. The sequence is unbounded.

Examples

			a(22) = 4 because
  22 mod 1 = 0 where r = 0,
  22 mod 2 = 0 where r = 0,
  22 mod 3 = 1 where 3 - 1 is even,
  22 mod 4 = 2 where 4 - 2 is even, but
  22 mod 5 = 2 where r > 0 and 5 - 2 is odd.
		

Links

• Martin Janecke, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A281072.

Programs

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