A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.

1, 4, 3, 11, 15, 13, 17, 24, 23, 73, 101, 104, 103, 111, 115, 113, 117, 124, 123, 173, 323, 373, 1104, 1103, 1111, 1115, 1113, 1117, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373

Offset: 3

Author

Peter Kolbus (peter(AT)kolbusfamily.com), Mar 11 2003

Keywords

• easy
• nonn
• word
• fini

Comments

In this version 101 is written "one hundred one", etc.

This uses the conventions that "and" is never used and two-digit numbers are not used before "hundred". The sequence is labeled "finite" because there is no widely accepted naming convention for arbitrarily large numbers. - David Wasserman, Dec 20 2004

Examples

			The 3rd term has 5 letters; the smallest positive integer with this number of letters is 3 (three).
		

Links

• Hans Havermann, Table of n, a(n) for n = 3..758
• Hans Havermann, Growth illustration for this sequence

Crossrefs

Cf. A001166, A052196 (the 'largest' analog of this sequence), A084390.

Programs

Mathematica

(* Works for a(n) up to 10^k *)
k=5;name[n_]:=IntegerName[n,"Words"];
nameLen[n_]:=StringLength[StringReplace[name[n],{" "-> "","-"-> "",","-> ""}]];
max[n_]:=Max[nameLen/@Range[10^(n-1)+1,10^n]];max10toK=max/@Range[k];
pos[n_Integer/;n>2]:=Position[Sort[Append[max10toK,n]],n,1][[1,1]]-1;
a[n_Integer/;n>2&&n<(10^k)+1]:=Module[{l=10^pos[n]},While[nameLen[l]!=n,l++];l];
a/@Range[3,40] (* Ivan N. Ianakiev, Sep 05 2018 *)

Extensions

Corrected by James Ong (blackshadowshade(AT)yahoo.com.au), Jun 27 2003

More terms from Brian Galebach, Feb 06 2004

Edited by David Wasserman, Dec 20 2004