%I #27 Sep 12 2018 16:56:18

%S 1,4,3,11,15,13,17,24,23,73,101,104,103,111,115,113,117,124,123,173,

%T 323,373,1104,1103,1111,1115,1113,1117,1124,1123,1173,1323,1373,3323,

%U 3373,11373,13323,13373,17373,23323,23373,73373,101373,103323,103373,111373

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

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

%C 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

%H Hans Havermann, <a href="/A080777/b080777.txt">Table of n, a(n) for n = 3..758</a>

%H Hans Havermann, <a href="http://chesswanks.com/seq/a080777.html">Growth illustration for this sequence</a>

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

%t (* Works for a(n) up to 10^k *)

%t k=5;name[n_]:=IntegerName[n,"Words"];

%t nameLen[n_]:=StringLength[StringReplace[name[n],{" "-> "","-"-> "",","-> ""}]];

%t max[n_]:=Max[nameLen/@Range[10^(n-1)+1,10^n]];max10toK=max/@Range[k];

%t pos[n_Integer/;n>2]:=Position[Sort[Append[max10toK,n]],n,1][[1,1]]-1;

%t a[n_Integer/;n>2&&n<(10^k)+1]:=Module[{l=10^pos[n]},While[nameLen[l]!=n,l++];l];

%t a/@Range[3,40] (* _Ivan N. Ianakiev_, Sep 05 2018 *)

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

%K easy,nonn,word,fini

%O 3,2

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

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

%E More terms from _Brian Galebach_, Feb 06 2004

%E Edited by _David Wasserman_, Dec 20 2004