A362506 a(n) is the least x >= 0 such that A362505(n) = x * y for some y with the same set of decimal digits as x.

0, 1, 2, 3, 1, 4, 5, 6, 2, 7, 8, 9, 3, 10, 1, 11, 12, 13, 4, 14, 15, 12, 16, 5, 17, 18, 19, 6, 20, 13, 21, 2, 22, 23, 7, 14, 24, 25, 26, 8, 27, 23, 15, 28, 29, 9, 30, 31, 16, 3, 10, 24, 10, 32, 33, 10, 1, 34, 17, 11, 35, 36, 25, 12, 37, 38, 12, 18, 34, 12, 13

Offset: 1

Author

Rémy Sigrist, Apr 23 2023

Keywords

• nonn
• base

Examples

			The first terms, alongside the corresponding y and A362505(n), are:
  n   a(n)  y    A362505(n)
  --  ----  ---  ----------
   1     0    0           0
   2     1    1           1
   3     2    2           4
   4     3    3           9
   5     1   11          11
   6     4    4          16
   7     5    5          25
   8     6    6          36
   9     2   22          44
  10     7    7          49
  11     8    8          64
  12     9    9          81
  13     3   33          99
  14    10   10         100
  15     1  111         111
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 100000 terms

Crossrefs

Cf. A362505.

Programs

PARI

{ print1(0); for (k = 1, 1469, fordiv (k, x, if (Set(digits(x)) == Set(digits(k/x)), print1 (", "x); break))) }

Python

from sympy import divisors
from itertools import count
def agen(): # generator of terms
    yield 0
    for n in count(1):
        for x in divisors(n):
            if set(str(x)) == set(str(n//x)):
                yield x
                break
print(list(islice(agen(), 71))) # Michael S. Branicky, Apr 23 2023