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Thursday, 21 March 2024

A Sequence With Only Eight Members

The idea popped into my head to look for numbers that together with their prime factors contain all the digits exactly once. This proved to be a relatively straight forward exercise. Up to one million, there are only eight numbers that qualify. These numbers together with their factorisations are as follows (permalink):

  • 10968=23×3×457
  • 28651=7×4093
  • 43610=2×5×72×89
  • 48960=26×32×5×17
  • 50841=33×7×269
  • 65821=7×9403
  • 80416=25×7×359
  • 90584=23×132×67
If repeated prime factors are disallowed, then only 28651 and 65821 qualify. These eight numbers, as I subsequently discovered, make up OEIS A124668:


 A124668

Numbers that together with their prime factors contain every digit exactly once.



So this is the sequence with only eight members: 10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584.

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