A231169 - OEIS

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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,...

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

(list; table; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=0..119.

OEIS Index entries for sequences related to the English name of numbers

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

Adjacent sequences: A231166 A231167 A231168 * A231170 A231171 A231172

KEYWORD

nonn,word,tabl

AUTHOR

M. F. Hasler, Nov 04 2013

STATUS

approved