A245062 Array read by upward antidiagonals: Niven (or Harshad) numbers arranged in rows by their digit sums.

1, 2, 10, 3, 20, 100, 4, 12, 110, 1000, 5, 40, 21, 200, 10000, 6, 50, 112, 30, 1010, 100000, 7, 24, 140, 220, 102, 1100, 1000000, 8, 70, 42, 230, 400, 111, 2000, 10000000, 9, 80, 133, 60, 320, 1012, 120, 10010, 100000000, 190, 18, 152, 322, 114, 410, 1120, 201, 10100, 1000000000

Offset

1,2

Comments

The n-th row contains in increasing order all multiples of n with digit sum n.

See A005349 for definitions and references.

Links

Alois P. Heinz, Antidiagonals n = 1..70, flattened

Eric W. Weisstein, Harshad Number, from MathWorld.

Example

Array begins as:
  1  10  100  1000  10000  100000  1000000  10000000  100000000  1000000000
  2  20  110   200   1010    1100     2000     10010      10100       11000
  3  12   21    30    102     111      120       201        210         300
  4  40  112   220    400    1012     1120      1300       2020        2200
  5  50  140   230    320     410      500      1040       1130        1220
  6  24   42    60    114     132      150       204        222         240
  7  70  133   322    511     700     1015      1141       1204        1330
  8  80  152   224    440     512      800      1016       1160        1232
  9  18   27    36     45      54       63        72         81          90
190 280  370   460    550     640      730       820        910        1090

Crossrefs

Cf. A002998 (column 1), A245065 (column 2).

Cf. A011557 (row 1), A069537 (row 2), A052217 (row 3), A063997 (row 4), A069540 (row 5), A062768 (row 6), A063416 (row 7), A069543 (row 8), A052223 (row 9).

Cf. A082260 (main diagonal).

Cf. A007953, A005349 (Niven or Harshad numbers).

Cf. A082259.

Sequence in context: A249917 A176577 A247476 * A120862 A153273 A276486

Adjacent sequences: A245059 A245060 A245061 * A245063 A245064 A245065

Keyword

nonn,base,tabl

Author

L. Edson Jeffery, Jul 10 2014

Status

approved