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A231270
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Irregular table read by rows r=0,1,2..., which contain the list of numbers whose (American) English name has no letter in common with that of r.
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1
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6, 50, 56, 60, 66, 6, 30, 36, 50, 56, 60, 66, 5, 6, 7, 9, 11, 500, 505, 506, 507, 509, 511, 600, 605, 606, 607, 609, 611, 700, 705, 706, 707, 709, 711, 900, 905, 906, 907, 909, 911, 6, 6000000, 6000006, 6000000000, 6000000006, 6006000000, 6006000006
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Row lengths are given in A227857. See there for links (motivation) and further discussion.
I conjecture that the table is finite and ends with row 6000000000000000000006006000006 having the entry [3], see examples and the (supposed) complete list given in the links section.
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LINKS
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EXAMPLE
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row 0: zero => six, fifty, fifty-six, sixty, sixty-six.
row 1: one => six, thirty, thirty-six, fifty, fifty-six, sixty, sixty-six.
row 2: two => five, six, seven, nine, eleven, five hundred, five hundred five, ..., nine hundred eleven.
row 3: three => six, six million, six million six, six billion, six billion six, six billion six million, six billion six million six, six nonillion, ..., six nonillion six billion six million six.
row 4: four => six,seven,eight,nine,ten,eleven,twelve,......
row 5: five => two, two thousand, two thousand two.
Row 13 and row 15 are the first empty rows, i.e., of length 0, i.e., row 12 [4, 6] is followed by data for row 14 [6], then row 16 [4].
Most rows for larger numbers are empty, e.g. 145..199, 245..299, ..., 712..899, 912..1999. After row 2002 [5], the only nonempty rows are those listed in row 3, containing only [3].
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PROG
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(PARI) {row(n, lang=English/*see A052360*/, LIM=999, start=0, step=1, verbose=0)=n==5 & LIM+=2000; n==3 && return(vector(15, i, 6*sum(j=0, 3, bittest(i, j)*10^[0, 6, 9, 30][j+1])))/*special case: cannot be computed by "brute force*/; my(a=[], w=lang(n)); verbose&&print1(w, " => "); w=Set(Vec(w)); forstep(k=start, LIM, step, setintersect( Set(Vec(lang(k))), w) || (verbose>1&&print1( lang(k)", ")) || a=concat(a, k)); a}
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CROSSREFS
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KEYWORD
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nonn,word,fini
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AUTHOR
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STATUS
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approved
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