This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A231169 #6 Nov 07 2013 03:29:54
%S A231169 4,2,3,1,1,3,2,1,1,4,2,1,1,1,4,1,1,0,1,1,4,0,0,0,0,0,1,3,1,2,0,1,0,2,
%T A231169 1,4,1,1,1,3,0,2,1,1,5,1,2,0,1,0,2,1,2,2,3,1,2,1,2,0,1,0,2,2,2,3,1,2,
%U A231169 0,1,0,2,0,3,1,2,2,4,1,1,2,2,0,2,0,2,2,1,2,3,5,2,2,1,4,1,2,1,2,4,3,3,2,2,6,3,3,2,3,4,2,0,2,2,2,3,2,2,4,7
%N A231169 Triangle read by rows: T[i,j] = number of (distinct) letters which the English names of i and j have in common; j=0,...,i ; i=0,1,2,...
%C A231169 This uses American English: no additional "and", i.e., "one hunded one", and short scale (10^9 = billion). Spaces and hyphens are ignored.
%C A231169 The diagonal yields the number of distinct letters in the (American) English name of the numbers (not A005589, which counts letters with multiplicity, or A052360 which even counts hyphens and spaces).
%C A231169 All numbers beyond 911 share at least one letter with any other number, except for 2000 and 2002 which don't share a letter with five. See A227857(n) for the number of numbers which have no letter in common with n.
%H A231169 <a href="/index/El#English">OEIS Index entries for sequences related to the English name of numbers</a>
%e A231169 The triangle reads:
%e A231169 row 0: 4; ("zero" and "zero" have the 4 letters "e", "o", "r" and "z" in common)
%e A231169 row 1: 2, 3; ("zero" and "one" have {e,o} in common, "one" and "one" have {e,n,o} in common)
%e A231169 row 2: 1, 1, 3; (common(two,zero)={o}, common(two,one)={o}, common(two,two)={o,t,w})
%e A231169 row 3: 2, 1, 1, 4; (common(three,three)={e,h,r,t})
%e A231169 etc.
%o A231169 (PARI) A231169(m,n,L=English/*see A052360*/,X=Vec(" -"))= #setintersect(setminus(Set(Vec(L(m))),X),Set(Vec(L(n))))
%K A231169 nonn,word,tabl
%O A231169 0,1
%A A231169 _M. F. Hasler_, Nov 04 2013