

A080777


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


9



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
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OFFSET

3,2


COMMENTS

In this version 101 is written "one hundred one", etc.
This uses the conventions that "and" is never used and twodigit 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^(n1)+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



