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A124172 Triangle in which row n contains values from 1 to n in alphabetical order (in English).

%I A124172 #22 Aug 17 2024 23:05:16
%S A124172 1,1,2,1,3,2,4,1,3,2,5,4,1,3,2,5,4,1,6,3,2,5,4,1,7,6,3,2,8,5,4,1,7,6,
%T A124172 3,2,8,5,4,9,1,7,6,3,2,8,5,4,9,1,7,6,10,3,2,8,11,5,4,9,1,7,6,10,3,2,8,
%U A124172 11,5,4,9,1,7,6,10,3,12,2,8,11,5,4,9,1,7,6,10,13,3,12,2
%N A124172 Triangle in which row n contains values from 1 to n in alphabetical order (in English).
%C A124172 This is a fractal sequence: if the first instance of each number is deleted, the original sequence is recovered. - _Franklin T. Adams-Watters_, Nov 24 2013
%C A124172 While it is unlikely to ever make a practical difference, for the sake of definiteness we specify that standard American number names are to be used. - _Franklin T. Adams-Watters_, Nov 24 2013
%C A124172 For 100th row, "one"=50th value and "one hundred"=51st value, placing the extremes in the center. - _Peter Woodward_, Jun 27 2015
%C A124172 We distinguish two kinds of "alphabetical order": letter-by-letter and word-by-word. For example, the a- and b-files in A340671, as well as my Mathematica code below (wherein you can make k any integer up to an arbitrary klimit), assume word-by-word (i.e., a space precedes any letter). For A124172 the assumption first impacts a(319602) = 800 (not 18). Ross Eckler first noted the sequence in the February 1981 issue of Word Ways (see p. 20 in the link), attributing it to Philip Cohen. - _Hans Havermann_, Aug 13 2024
%H A124172 A. Ross Eckler, <a href="https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=2556&amp;context=wordways">Alphabetizing the Integers</a> (Word Ways, 1981, Vol. 14, No. 1, pp. 18-20).
%e A124172 Triangle begins:
%e A124172   1,
%e A124172   1,2,
%e A124172   1,3,2,
%e A124172   4,1,3,2
%e A124172   5,4,1,3,2
%e A124172   5,4,1,6,3,2,
%e A124172   ...
%t A124172 names = {"one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen"}; Flatten[Table[Table[Position[names, Sort[Take[names, n]][[i]], 1, 1][[1, 1]], {i, n}], {n, Length[names]}]] (* _T. D. Noe_, Nov 25 2013 *)
%t A124172 klimit=100; u=IntegerName[Range[klimit],"Words"]; k=24; seq={}; Do[r=Take[u,i]; s=AlphabeticSort[r]; t=Table[FirstPosition[r,s[[j]]][[1]],{j,i}]; seq=Join[seq,t],{i,k}]; seq (* _Hans Havermann_, Aug 13 2024 *)
%Y A124172 Cf. A002260, A340671.
%K A124172 nonn,tabl,word
%O A124172 1,3
%A A124172 _Colm Mulcahy_, Dec 05 2006
%E A124172 Edited name and more terms from _Franklin T. Adams-Watters_, Nov 24 2013