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In Metropolis, all bus routes are numbered with a number >10, but not all numbers are used.

Buses 33, 55, 222, and the special 55555, and only those buses, go to the airport. All the buses that go to the airport, and only those buses, are numbered such that all digits are the same. The local taxi service (phone #777-7777) also goes to the airport.

What is a concise way of describing a number with multiple digits that are all the same digit?

Under 100, I would call them "multiples of 11." Is there a word for the more general class, narrower than "palindrome?"

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2 Answers 2

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10

They are known as repdigits.

The article states it is implicitly valid for at least base 10, but it easily generalises for all bases:

eg:

  • bin 111 = 7 (which is a repdigit either way)
  • hex CCC = 3276
  • oct 777 = 511

With x being the digit to be repeated, B the base and y the number of repeats, in base 10 a repdigit can be calculated thusly:

enter image description here

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  • There is also the potential that: a. I think that capitalising is appropriate in this case, and b. It's some form of typo. In this case it's more the latter, I copied and pasted it from wikipedia directly :)
    – Lamar Latrell
    Oct 4, 2015 at 3:42
  • Interesting. But how well known generally? Most dictionaries that have it say that its usage is in "recreational mathematics". Several mainstream dictionaries (Merriam-Webster, Collins, Oxford Dictionaries) don't list it at all. So it might not be commonly used among transit system administrators (or riders!)
    – Brian Hitchcock
    Oct 4, 2015 at 13:37
  • I'd be more inclined to spell it out, say, as "repeated digit number"; The "digit" being singular, because the same digit repeats (rather than several digits repeating as in the fraction 1/7 = 0.1428571428571428...)
    – Brian Hitchcock
    Oct 4, 2015 at 13:43
  • It seems to me that bin 111 = 7, not 8.
    – WBT
    Aug 5, 2022 at 17:25
  • True! Not sure how that sneaked in 😳
    – Lamar Latrell
    Aug 6, 2022 at 0:04
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It's called a Nelson. 222 is called Two Nelson and 333 is called Three Nelson

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  • What about 33 and 55?
    – KillingTime
    Aug 4, 2022 at 12:31
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    I was able to verify "Nelson", so I added a link for that (but I didn't find "two Nelson", only "double Nelson"). It's definitely not a term I've heard before; can you add any evidence it's used outside cricket?
    – Laurel ♦
    Aug 4, 2022 at 12:37

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