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

%I A080777 #27 Sep 12 2018 16:56:18
%S A080777 1,4,3,11,15,13,17,24,23,73,101,104,103,111,115,113,117,124,123,173,
%T A080777 323,373,1104,1103,1111,1115,1113,1117,1124,1123,1173,1323,1373,3323,
%U A080777 3373,11373,13323,13373,17373,23323,23373,73373,101373,103323,103373,111373
%N A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.
%C A080777 In this version 101 is written "one hundred one", etc.
%C A080777 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 A080777 Hans Havermann, <a href="/A080777/b080777.txt">Table of n, a(n) for n = 3..758</a>
%H A080777 Hans Havermann, <a href="http://chesswanks.com/seq/a080777.html">Growth illustration for this sequence</a>
%e A080777 The 3rd term has 5 letters; the smallest positive integer with this number of letters is 3 (three).
%t A080777 (* Works for a(n) up to 10^k *)
%t A080777 k=5;name[n_]:=IntegerName[n,"Words"];
%t A080777 nameLen[n_]:=StringLength[StringReplace[name[n],{" "-> "","-"-> "",","-> ""}]];
%t A080777 max[n_]:=Max[nameLen/@Range[10^(n-1)+1,10^n]];max10toK=max/@Range[k];
%t A080777 pos[n_Integer/;n>2]:=Position[Sort[Append[max10toK,n]],n,1][[1,1]]-1;
%t A080777 a[n_Integer/;n>2&&n<(10^k)+1]:=Module[{l=10^pos[n]},While[nameLen[l]!=n,l++];l];
%t A080777 a/@Range[3,40] (* _Ivan N. Ianakiev_, Sep 05 2018 *)
%Y A080777 Cf. A001166, A052196 (the 'largest' analog of this sequence), A084390.
%K A080777 easy,nonn,word,fini
%O A080777 3,2
%A A080777 Peter Kolbus (peter(AT)kolbusfamily.com), Mar 11 2003
%E A080777 Corrected by James Ong (blackshadowshade(AT)yahoo.com.au), Jun 27 2003
%E A080777 More terms from _Brian Galebach_, Feb 06 2004
%E A080777 Edited by _David Wasserman_, Dec 20 2004