# What do you call a number with no repeating digits?

A word with no repeated characters is called an isogram.

Is there a word for a number with no repeating digits?

For example: 123 is a ____.

To clarify further, for a decimal number system the number could never be longer than 10 digits and for any other base number system the number could never be longer than the total number of distinct symbols in that number system.

• Can your number be longer than 10 digits? Jan 23, 2019 at 3:21
• Are you sure "isogram" cannot be used for this? Jan 30, 2019 at 13:52
• Interestingly, the OED doesn't have this definition for isogram, only a definition relating to diagrams with some equality of feature. Presumably when the entry is updated this new coinage will be reflected. If you wanted to form your own word, since isogram comes from Greek ἴσος ("equal") + γράμμα ("letter") I think isarithm seems likely, substituting αριθμός ("number") for the second part. (Of course, based on the etymology of the word, I would have thought that toot and mama would also qualify as isograms, having an equal number of each letter.) Feb 6, 2019 at 22:08
• @1006a 'If you wanted to form your own word' belongs on the 'fiction' sites, not on English Language and (present accepted) Usage. 'Word' means more than 'string of umpteen letters, surrounded by white spaces, pronounceable and perhaps showing connection with Latin etc roots'. May 30, 2019 at 13:52
• @1006a: I don’t mind making up words where no existing word can be attested. But wouldn’t isopsifi be preferable? The digit / figure versus number distinction also exists in Greek: ψηφίο versus αριθμός. Aug 8, 2019 at 23:04

The set of all numbers with no repeating digits is sequence A010784 in the Online Encyclopedia of Integer Sequences. On OEIS, such a number is called a xenodrome.

This word is made of the prefix xeno-, meaning "alien," with the root drome, meaning "running, course, race track." It was probably coined by analogy with "palindrome" (with the etymological meaning "running back"), and I suppose the notion is that as you run from one end of the number to the other, every digit you encounter is an alien.

However, this word seems to be extremely rare; it was probably coined by OEIS contributors and it hasn't spread far from there. The only other usage of this word I was able to find in a Google search was the Stack Exchange post "All the Xenodromes," which almost certainly got the word directly from OEIS.

• Please add substantiating references from reputable sources. Oct 27, 2019 at 18:01
• @Edwin For the word itself, OEIS seems to be the most reputable source which has ever used it. Should I add references for the meanings of "xeno-" and "drome" as well? Oct 27, 2019 at 18:13
• The OEIS is a reputable source. Oct 27, 2019 at 18:17
• @Lambie It may be for subject-specific issues, but ELU looks at standard English usage. Is 'xenodrome' in a reputable dictionary? We used '1010 acid', a well-known label, when I was working in a research lab, but it's hardly a term that is suitable to suggest as a 'word' on a site for people looking at non-niche English. MathematicsSE, maybe. Oct 27, 2019 at 19:56
• @EdwinAshworth Not my circus, not my monkeys. But, it hardly seems that common usage is the standard for this site. Otherwise, we'd be called English Language and Common Usage StackExchange. I will grant that there doesn't seem to be a better source than OEIS, but if this an accepted technical term, it is just that. Accepted. Oct 27, 2019 at 20:24

It's not a single word, but the very unsatifactory answer is isogram number. You can find it in these less-than-reputable sources.

• That could work, but I'm not sure about the applicability of this description, which appears similarly in both links: "Can you name the only whole numbers with no repeating letters in their name?" It seems to refer to spelling numbers. Would inverting it ("numeral isogram," with numeral as an adjective describing that the characters to be counted are digits and not letters) work better? Feb 6, 2019 at 21:35

Is this what you are referring to?

## repetend [ rep-i-tend, rep-i-tend ] / ˈrɛp ɪˌtɛnd, ˌrɛp ɪˈtɛnd /

noun

1. Mathematics. the part of a repeating decimal that is repeated, as 1234 in 0.123412341234. …

2. Music. a phrase or sound that is repeated.

3. Prosody. a word, phrase, line, or longer element that is repeated, sometimes with variation, at irregular intervals in a poem.

or:

## Full Repetend Prime

A prime 𝑝 for which ¹⁄𝑝 has a maximal period decimal expansion of p − 1 digits. Full reptend primes are sometimes also called long primes (Conway and Guy 1996, pp. 157–163 and 166–171). There is a surprising connection between full reptend primes and Fermat primes.