A052196 Largest natural number less than 10^66 requiring exactly n letters in English.

10, 9, 60, 90, 70, 66, 96, 10000000000, 10000000000000, 10000000000000000000000000000000000, 10000000000000000000000000, 10000000000000000000000000000000000000, 10000000000000000000000000000000000000000000000000000000000000000, 9000000000000000000000000000000000000000000000000000000000000000

Offset

3,1

Comments

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.

Links

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.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A001166, A080777.

Sequence in context: A237114 A217412 A241285 * A243035 A070252 A038311

Adjacent sequences: A052193 A052194 A052195 * A052197 A052198 A052199

Keyword

nonn,word,fini,full

Author

Henry Bottomley, Jan 28 2000

Extensions

a(11) from Brian Galebach, Feb 06 2004

Edited and extended by Hans Havermann, Nov 08 2013

Status

approved