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

Author

Henry Bottomley, Jan 28 2000

Keywords

• nonn
• word
• fini
• full

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.

Examples

			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
		

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.

Crossrefs

Cf. A001166, A080777.

Programs

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 *)

Extensions

a(11) from Brian Galebach, Feb 06 2004

Edited and extended by Hans Havermann, Nov 08 2013