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A231270 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.

%I A231270 #10 Nov 06 2013 10:33:39
%S A231270 6,50,56,60,66,6,30,36,50,56,60,66,5,6,7,9,11,500,505,506,507,509,511,
%T A231270 600,605,606,607,609,611,700,705,706,707,709,711,900,905,906,907,909,
%U A231270 911,6,6000000,6000006,6000000000,6000000006,6006000000,6006000006
%N A231270 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.
%C A231270 Row lengths are given in A227857. See there for links (motivation) and further discussion.
%C A231270 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.
%H A231270 M. F. Hasler, <a href="/A231270/a231270.txt">List of n, row(n) for all nonempty rows</a>.
%e A231270 row 0: zero => six, fifty, fifty-six, sixty, sixty-six.
%e A231270 row 1: one => six, thirty, thirty-six, fifty, fifty-six, sixty, sixty-six.
%e A231270 row 2: two => five, six, seven, nine, eleven, five hundred, five hundred five, ..., nine hundred eleven.
%e A231270 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.
%e A231270 row 4: four => six,seven,eight,nine,ten,eleven,twelve,......
%e A231270 row 5: five => two, two thousand, two thousand two.
%e A231270 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].
%e A231270 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].
%o A231270 (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}
%Y A231270 Cf. A227857, A231169.
%K A231270 nonn,word,fini
%O A231270 0,1
%A A231270 _M. F. Hasler_, Nov 06 2013