Erdos Woods Numbers -- #A059756

[hv at crypt.org]

Thanks to both Victor and Rainer for the clarifications.

I think the description in OEIS could do with improvement. One approach
would be a more mathematical definition:

  k is in a() if there exists an n such that for all 0 <= i <= k, either
  gcd(n, n+i) > 1 or gcd(n+i, n+k) > 1 (or both).

.. or alternatively make it clearer that these are "possible lengths",
and that if a number is missing from the list that implies no sequence
is possible of that length:
  2 is not in the list, since there is no sequence [a, a+1, a+2] such
  that a+1 has a factor in common with either a or a+2.

(Or both.)


victor at idaccr.org (Victor S. Miller) wrote:
:And, I agree with you, 1 is trivially an Erdos Woods number, since the
:open interval is empty.

while Rainer Rosenthal <r.rosenthal at web.de> wrote:
[No.] Because neighbours never have a common factor > 1.

If I've (now) correctly understood, we need only have a common
factor with _one_ endpoint. so for the interval [2, 3], 2 has a
common factor with 2, and 3 with 3.

Hugo