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.

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

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..47.

M. F. Hasler, List of n, row(n) for all nonempty rows.

Example

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].

Prog

(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}

Crossrefs

Cf. A227857, A231169.

Sequence in context: A212232 A187670 A187462 * A062801 A035290 A138422

Adjacent sequences: A231267 A231268 A231269 * A231271 A231272 A231273

Keyword

nonn,word,fini

Author

M. F. Hasler, Nov 06 2013

Status

approved