A330898 Positive numbers k of the form x*y where k, x and y have the same set of decimal digits.

1, 11, 100, 111, 1000, 1010, 1100, 1111, 10000, 10010, 10100, 10110, 11000, 11010, 11100, 11110, 11111, 31003, 99190, 100000, 100010, 100100, 100110, 101000, 101010, 101100, 101101, 101110, 110000, 110010, 110100, 110110, 111000, 111010, 111100, 111111, 266616

Offset: 1

Author

Rémy Sigrist, May 01 2020

Keywords

• nonn
• base

Comments

If k belongs to the sequence, then 100*k also belongs to the sequence.

The positive repunits belong to the sequence.

The first pandigital term is 1047463798950190521 = 1023456789^2.

Examples

			The first terms, alongside an appropriate factorization and the corresponding set of digits, are:
  n   a(n)    x    y       digits(n)
  --  ------  ---  ------  ---------
   1       1    1       1  {1}
   2      11    1      11  {1}
   3     100   10      10  {0, 1}
   4     111    1     111  {1}
   5    1000   10     100  {0, 1}
   6    1010   10     101  {0, 1}
   7    1100   10     110  {0, 1}
   8    1111    1    1111  {1}
   9   10000   10    1000  {0, 1}
  10   10010   10    1001  {0, 1}
  11   10100   10    1010  {0, 1}
  12   10110   10    1011  {0, 1}
  13   11000   10    1100  {0, 1}
  14   11010   10    1101  {0, 1}
  15   11100   10    1110  {0, 1}
  16   11110  101     110  {0, 1}
  17   11111    1   11111  {1}
  18   31003  103     301  {0, 1, 3}
  19   99190  109     910  {0, 1, 9}
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002275, A086066.

Programs

PARI

is(n) = { my (s=Set(digits(n))); fordiv (n, d, if (Set(digits(d))==s && Set(digits(n/d))==s, return (1))); return (0) }