A231169 - OEIS

%I #6 Nov 07 2013 03:29:54

%S 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 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 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 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 This uses American English: no additional "and", i.e., "one hunded one", and short scale (10^9 = billion). Spaces and hyphens are ignored.

%C 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 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 <a href="/index/El#English">OEIS Index entries for sequences related to the English name of numbers</a>

%e The triangle reads:

%e row 0: 4; ("zero" and "zero" have the 4 letters "e", "o", "r" and "z" in common)

%e row 1: 2, 3; ("zero" and "one" have {e,o} in common, "one" and "one" have {e,n,o} in common)

%e row 2: 1, 1, 3; (common(two,zero)={o}, common(two,one)={o}, common(two,two)={o,t,w})

%e row 3: 2, 1, 1, 4; (common(three,three)={e,h,r,t})

%e etc.

%o (PARI) A231169(m,n,L=English/*see A052360*/,X=Vec(" -"))= #setintersect(setminus(Set(Vec(L(m))),X),Set(Vec(L(n))))

%K nonn,word,tabl

%O 0,1

%A _M. F. Hasler_, Nov 04 2013