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If I am speaking to somebody about 4 digit numbers in specific format where the second and the third digits are the same or where the first and the third digits are the same what would be the term for them?

hyperscience
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  • Simply try $m=1010n$ or $n=1001n$ for $n-=0,1,2,\cdots,9$ – Mostafa Ayaz Nov 03 '18 at 08:17
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    Who would "waste" a term to denote a set of twenty specific, but somewhat dull numbers? – Hagen von Eitzen Nov 03 '18 at 08:23
  • Maybe a palindrome? or a palindrome of length $4$ in this case. – Yanko Nov 03 '18 at 09:26
  • "to denote a set of twenty specific, but somewhat dull numbers" the are 171 of them, not 20. But yes, they are quite dull. – fleablood Nov 08 '18 at 19:04
  • The first group of the form $abba$ are "four digit palidromes" and the second group of the form $abab$ are "four digit multiples of $101$." – fleablood Nov 08 '18 at 19:05
  • Oh, wait! You mean numbers of the form $abbc$ or $abac$. There is utterly no reason to expect anybody to have bothered to make up a term for something like that. We can call them "betterday numbers" if you like, but it'd be up to you to educate people on the term. Don't forget "fleablood numbers" are numbers where the second digit is the square of the fifth digit. – fleablood Nov 08 '18 at 19:14
  • You wrote: where the second and the third digits are the same or where the first and the third digits are the same Your examples are more like where the second and the third digits are the same AND where the first and fourth digits are the same, etc. – mike65535 Nov 08 '18 at 19:27

2 Answers2

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If you consider your four digit numbers as words on the alphabet $\{0, 1, \dots, 9\}$, the words of the first category are of the form $uu^r$ (where $u^r$ denotes the reverse of $u$, that is, $u$ read from right to left, if you prefer) and are called palindromes. The words of the second category are of the form $uu$ and are called squares. Of course this terminology is only used in theoretical computer science and would be ambiguous for a number.

J.-E. Pin
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The term would be "4 digit numbers where the second and the third digits are the same or where the first and the third digits are the same"

fleablood
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