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A052196
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Largest natural number less than 10^66 requiring exactly n letters in English.
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3
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10, 9, 60, 90, 70, 66, 96, 10000000000, 10000000000000, 10000000000000000000000000000000000, 10000000000000000000000000, 10000000000000000000000000000000000000, 10000000000000000000000000000000000000000000000000000000000000000, 9000000000000000000000000000000000000000000000000000000000000000
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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3,1
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COMMENTS
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This uses US nomenclature: no conjunctive 'and'; 10^10 = 'ten billion'.
This is the 'largest' counterpart to A080777, which gives the smallest positive integer with exactly n letters.
Because of the definition's size limitation, a(758) will be the largest term in this finite sequence; a(758) = 878878878878878878878878878878878878878878878878878878878878878878.
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LINKS
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Hans Havermann, Table of n, a(n) for n = 3..758
Hans Havermann, Growth illustration for this sequence
Hans Havermann, Define, divide, and conquer
Pegg, E. Jr. and Weisstein, E. W. Mathematica's Google Aptitude: problem #20 MathWorld Headline news, Oct 13, 2004.
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EXAMPLE
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The largest numbers (<10^66) using 10 to 15 letters:
10: 10*10^9 = ten billion
11: 10*10^12 = ten trillion
12: 10*10^33 = ten decillion
13: 10*10^24 = ten septillion
14: 10*10^36 = ten undecillion
15: 10*10^63 = ten vigintillion
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MATHEMATICA
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k=100; lst=StringLength/@StringReplace[IntegerName/@Range[k],
{"-"-> "", " "-> ""}]; max[n_]:=Last[Position[lst, n]];
max/@Range[3, 9]//Flatten (* Ivan N. Ianakiev, Oct 07 2015 *)
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CROSSREFS
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Cf. A001166, A080777.
Sequence in context: A237114 A217412 A241285 * A243035 A070252 A038311
Adjacent sequences: A052193 A052194 A052195 * A052197 A052198 A052199
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KEYWORD
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nonn,word,fini,full
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AUTHOR
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Henry Bottomley, Jan 28 2000
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EXTENSIONS
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a(11) from Brian Galebach, Feb 06 2004
Edited and extended by Hans Havermann, Nov 08 2013
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STATUS
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approved
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