%N Numbers n such that the period of 1/n, or 0 if 1/n terminates, is strictly greater than the periods of the decimal expansions of 1/m beforehand.
%C This sequence is infinite because 1/(10^n-1) has a period of n for all n, so the period can be arbitrarily large.
%C Are 1, 3, 289 and 361 the only members that are not in A001913? - _Robert Israel_, Feb 10 2019
%H Robert Israel, <a href="/A306355/b306355.txt">Table of n, a(n) for n = 1..10000</a>
%F RECORDS transform of A051626.
%e 7 is a term because 1/7 has a period of 6, which is greater than the periods of 1/m for m<7.
%p count:= 1: A:= 1: m:= 0:
%p for k from 0 to 100 do
%p for d in [3,7,9,11] do
%p x:= 10*k+d;
%p p:= numtheory:-order(10,x);
%p if p > m then
%p m := p;
%p count:= count+1;
%p A[count]:= x
%p od od:
%p seq(A[i],i=1..count); # _Robert Israel_, Feb 10 2019
%Y Cf. A051626.
%Y Contains A001913.
%A _Matthew Schulz_, Feb 09 2019