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

3,2

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

Links

Hans Havermann, Table of n, a(n) for n = 3..758

Hans Havermann, Growth illustration for this sequence

Example

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

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 *)

Crossrefs

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

Sequence in context: A316966 A295727 A200073 * A001166 A065337 A257078

Adjacent sequences: A080774 A080775 A080776 * A080778 A080779 A080780

Keyword

easy,nonn,word,fini

Author

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

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

Status

approved