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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,...
2
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, 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, 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
OFFSET
0,1
COMMENTS
This uses American English: no additional "and", i.e., "one hunded one", and short scale (10^9 = billion). Spaces and hyphens are ignored.
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).
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.
EXAMPLE
The triangle reads:
row 0: 4; ("zero" and "zero" have the 4 letters "e", "o", "r" and "z" in common)
row 1: 2, 3; ("zero" and "one" have {e,o} in common, "one" and "one" have {e,n,o} in common)
row 2: 1, 1, 3; (common(two,zero)={o}, common(two,one)={o}, common(two,two)={o,t,w})
row 3: 2, 1, 1, 4; (common(three,three)={e,h,r,t})
etc.
PROG
(PARI) A231169(m, n, L=English/*see A052360*/, X=Vec(" -"))= #setintersect(setminus(Set(Vec(L(m))), X), Set(Vec(L(n))))
CROSSREFS
Sequence in context: A266141 A266147 A326046 * A297847 A145326 A178915
KEYWORD
nonn,word,tabl
AUTHOR
M. F. Hasler, Nov 04 2013
STATUS
approved