repdigit

English

WOTD – 20 August 2018

The number 7777 on this Washington, D.C., vehicle license plate is a repdigit

Etymology

Blend of rep(eated) +‎ digit.

Pronunciation

• (Received Pronunciation, General American) IPA^(key): /ˈɹɛpˌdɪd͡ʒɪt/

  • Audio (Southern England):

    (file)

• Hyphenation: rep‧di‧git

Noun

Examples
7 11 666 9,999

repdigit (plural repdigits)

1. (recreational mathematics) A number composed only of one or more occurrences of one specific digit and no other digit.
   • 1975, David W. Ballew, Ronald C. Weger, “Repdigit Triangular Numbers”, in Journal of Recreational Mathematics, volume 8, number 2, Farmingdale, N.Y.: Baywood Publishing Co., →ISSN, →OCLC, pages 96–98:

     Repdigit Triangular Numbers [article title]

   • 1980 January, Murray S[eymour] Klamkin, quoting Charles W. Trigg, “The Olympiad Corner: 11”, in Crux Mathematicorum, volume 6, number 1, Ottawa, Ont.: Canadian Mathematical Society, →ISSN, →OCLC, page 16:

     Is there any system of notation in which there is a repdigit $aa$ such that $(aa)^{2}=ccdd$, with $c=a-1$ and $d=c-1$?

   • 2002, Clifford A[lan] Pickover, “Gallery I: Squares, Cubes, and Tesseracts”, in The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton, N.J., Woodstock, Oxfordshire: Princeton University Press, →ISBN, page 284:

     Here is another palindromic magic square that has the added property of having main diagonals containing eight repeating "repdigits": 222, 333, 444, 555, 666, 777, 888, and 999. The magic sum is 2442.

   • 2005, James J[oseph] Tattersall, “Modular Arithmetic”, in Elementary Number Theory in Nine Chapters, 2nd edition, Cambridge: Cambridge University Press, →ISBN, section 5.6 (Supplementary Exercises), paragraph 14, page 193:

     A positive with repeated digit is called a repdigit, for example 222, 55555, and all repunits are repdigits.

Hyponyms

• repunit

Translations

number composed of one digit

• Bulgarian: репдиджит (repdidžit)
• Chinese:

  Mandarin: 純位數 / 纯位数 (chúnwèishù)

• Esperanto: repdigito
• French: nombre uniforme m
• German: Schnapszahl (de) f
• Italian: numero a cifra ripetuta m
• Japanese: ぞろ目
• Korean: 렙디지트 (repdijiteu)
• Russian: репди́гиты (repdígity)
• Tamil: ஒற்றெண் (oṟṟeṇ)

See also

• repeating decimal
• repetend

References

• Eric W[olfram] Weisstein (2018 August 20 (last accessed)) “Repdigit”, in MathWorld‎^[1], archived from the original on 15 February 2018.

Further reading

• repdigit on Wikipedia.Wikipedia