Wikipedia:Reference desk/Archives/Mathematics/2014 December 21

= December 21 =

Two mathematical terms sought
What are the accepted terms for the following two types of numbers?


 * 1) The sequence 1, 3, 6, 10, 15, 21 . ..
 * 2) Numbers like 456, 2,345, 12,345, 45,678, 345,678, 987, 3,210, 65,432, 765,432, etc. Khemehekis (talk) — Preceding undated comment added 10:46, 21 December 2014 (UTC)


 * The first lot are the Triangular numbers. I don't know a special term for numbers where the digits are in sequence. Dmcq (talk) 11:39, 21 December 2014 (UTC)
 * Thanks for the term "triangular numbers". As for the latter group, I call them "stairstep numbers" in this thread. I want to know the "real" term, though. Khemehekis (talk) 12:15, 21 December 2014 (UTC)
 * A138141 ("Numbers with digits in ascending order that differ exactly by 1") and A138142 ("Nonnegative numbers with digits in descending order that differ exactly by 1") give no names. PrimeHunter (talk) 12:40, 21 December 2014 (UTC)
 * OK, then. I guess I'll just continue to use "stairstep number" (a translation of the Kankonian term bayet na tatz*emad). Much as I use the Kankonian "Wantas sequence" for the 1, 2, 6, 12, 60, 420, 840 . . . sequence. Khemehekis (talk) 13:32, 21 December 2014 (UTC)
 * Kankonian appears to be Khemehekis conlang. —Tamfang (talk) 01:14, 22 December 2014 (UTC)


 * Numbers formed by concatenating consecutive integers would include your examples as well as numbers such as 91,011. A subset of that is A007908  ("Concatenation of the numbers from 1 to n. "). -- ToE 21:24, 21 December 2014 (UTC)