Since I was a kid, I have always been amazed by the fact that when multiplying four or seven by three, the two products obtained have the same digits but in a different position.
3 x 4 = 12
3 x 7 = 21
Now that I'm a little older, not much, it still surprises me that there are numbers that when they are multiplied by two different numbers, its products are a permutation of each other. Apparently you can find a number for each pair of distinct numbers provided that one of these numbers is not a multiple of ten of the other (ie for n and n * 10 ^ m, there is no number that when multiplied by a specific number, its products are not anagrams).
Two years ago I published 8 sequences based on these facts in the OEIS. The title of each of these sequences is: a(n) =smallest number such a(n)*n is an anagram of a(n)* X .
For example the sequence for X equal to four is :
1782, 62937, 54, 1, 2826, 891, 3, 269, 631, 324, 2718, 4311, 3681, 37, 387, 25974, 4401, 477, 45, 48, 256437, 3393, 37, 26523, 3465, 3252, 3699, 34623, 2922, 27972, 27, 271, 284787, 27324, 25971, 263223, 26973, 25974, 2579247, 2514744 (OEIS A175693)
So:
1782 x 1 = 1782 and 1782 x 4 = 7218
62937 x 2 = 125874 and 62937 x 4 = 251748
54 x 3 = 162 and 54 x 4 = 216
and so on.
Sometimes the same number meets the condition for example:
37 x 13 = 481, 37 x 22 = 814, 37 x 4 = 148
If we write these numbers in a table:
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