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

1,2

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A281072.

Sequence in context: A214052 A276094 A247339 * A256908 A346466 A258409

Adjacent sequences: A281068 A281069 A281070 * A281072 A281073 A281074

Keyword

easy,nonn

Author

Martin Janecke, Jan 14 2017

Status

approved