A362505 Nonnegative numbers of the form x*y where x and y have the same set of decimal digits.

0, 1, 4, 9, 11, 16, 25, 36, 44, 49, 64, 81, 99, 100, 111, 121, 144, 169, 176, 196, 225, 252, 256, 275, 289, 324, 361, 396, 400, 403, 441, 444, 484, 529, 539, 574, 576, 625, 676, 704, 729, 736, 765, 784, 841, 891, 900, 961, 976, 999, 1000, 1008, 1010, 1024

Offset

1,3

Comments

Repunits (A002275), squares (A000290) and A330898 are subsequences.

Links

Table of n, a(n) for n=1..54.

Example

The first terms, alongside an appropriate factorization, are:
  n   a(n)  x   y
  --  ----  --  ---
   1     0   0    0
   2     1   1    1
   3     4   2    2
   4     9   3    3
   5    11   1   11
   6    16   4    4
   7    25   5    5
   8    36   6    6
   9    44   2   22
  10    49   7    7
  11    64   8    8
  12    81   9    9
  13    99   3   33
  14   100  10   10
  15   111   1  111

Prog

(PARI) is(n) = { if (n==0, 1, fordiv (n, x, if (Set(digits(x))==Set(digits(n/x)), return (1))); return (0)); }
(Python)
from sympy import divisors
def ok(n): return n == 0 or any(set(str(x)) == set(str(n//x)) for x in divisors(n))
print([k for k in range(1025) if ok(k)]) # Michael S. Branicky, Apr 23 2023

Crossrefs

Cf. A000290, A002275, A086066, A330898, A362506 (least x's).

Sequence in context: A316621 A336826 A212017 * A236171 A312838 A312839

Adjacent sequences: A362502 A362503 A362504 * A362506 A362507 A362508

Keyword

nonn,base

Author

Rémy Sigrist, Apr 23 2023

Status

approved