A389838 Numbers of the form j*k or j*k + (j-1)*(k-1) with j, k > 1.

4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..65.

António Martins-Tuválkin, How to arrange any number of stars on the U.S. flag; a broader definition of allowable arrangements that indicates that for any number k of stars > 0, one of four types of arrangement is applicable.

Example

a(1) = 4 stars on the corners of the unit square.
a(2) = 5 stars after putting an additional star in the center of that unit square.

Prog

(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}))

Crossrefs

Cf. A140646.

Complement of A005382, except 1.

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

Sequence in context: A335186 A257816 A033597 * A336379 A088720 A134848

Adjacent sequences: A389835 A389836 A389837 * A389839 A389840 A389841

Keyword

nonn

Author

Oliver Gramberg, Dec 17 2025

Status

approved