A389838 - OEIS

%I #41 Feb 03 2026 22:57:27

%S 4,5,6,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,

%T 30,32,33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72

%N Numbers of the form j*k or j*k + (j-1)*(k-1) with j, k > 1.

%C Numbers of stars which can be arranged on a flag so as either to completely fill a rectangle (j*k stars), or where one additional star is put in each unit square (j*k + (j-1)*(k-1) stars).

%H António Martins-Tuválkin, <a href="https://www.crwflags.com/fotw/flags/us_stars.html">How to arrange any number of stars on the U.S. flag</a>; a broader definition of allowable arrangements that indicates that for any number k of stars > 0, one of four types of arrangement is applicable.

%e a(1) = 4 stars on the corners of the unit square.

%e a(2) = 5 stars after putting an additional star in the center of that unit square.

%o (Python) print(sorted({v for max in [50] for j in range(2, max+1) for k in range(2, max+1) for v in (j*k, j*k+(j-1)*(k-1)) if v <= 2*max+1}))

%Y Cf. A140646.

%Y Complement of A005382, except 1.

%Y Superset of A001105 when starting there at position 2, superset of A053726.

%K nonn

%O 1,1

%A _Oliver Gramberg_, Dec 17 2025