cp's OEIS Frontend

A052196 Largest natural number less than 10^66 requiring exactly n letters in English.

%I A052196 #31 Feb 16 2025 08:32:41
%S A052196 10,9,60,90,70,66,96,10000000000,10000000000000,
%T A052196 10000000000000000000000000000000000,10000000000000000000000000,
%U A052196 10000000000000000000000000000000000000,10000000000000000000000000000000000000000000000000000000000000000,9000000000000000000000000000000000000000000000000000000000000000
%N A052196 Largest natural number less than 10^66 requiring exactly n letters in English.
%C A052196 This uses US nomenclature: no conjunctive 'and'; 10^10 = 'ten billion'.
%C A052196 This is the 'largest' counterpart to A080777, which gives the smallest positive integer with exactly n letters.
%C A052196 Because of the definition's size limitation, a(758) will be the largest term in this finite sequence; a(758) = 878878878878878878878878878878878878878878878878878878878878878878.
%H A052196 Hans Havermann, <a href="/A052196/b052196.txt">Table of n, a(n) for n = 3..758</a>
%H A052196 Hans Havermann, <a href="http://chesswanks.com/seq/a052196.html">Growth illustration for this sequence</a>
%H A052196 Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2013/11/define-divide-and-conquer_10.html">Define, divide, and conquer</a>
%H A052196 Pegg, E. Jr. and Weisstein, E. W. <a href="https://mathworld.wolfram.com/news/2004-10-13/google/">Mathematica's Google Aptitude: problem #20</a> MathWorld Headline news, Oct 13, 2004.
%e A052196 The largest numbers (<10^66) using 10 to 15 letters:
%e A052196 10: 10*10^9 = ten billion
%e A052196 11: 10*10^12 = ten trillion
%e A052196 12: 10*10^33 = ten decillion
%e A052196 13: 10*10^24 = ten septillion
%e A052196 14: 10*10^36 = ten undecillion
%e A052196 15: 10*10^63 = ten vigintillion
%t A052196 k=100;lst=StringLength/@StringReplace[IntegerName/@Range[k],
%t A052196 {"-"-> ""," "-> ""}];max[n_]:=Last[Position[lst,n]];
%t A052196 max/@Range[3,9]//Flatten (* _Ivan N. Ianakiev_, Oct 07 2015 *)
%Y A052196 Cf. A001166, A080777.
%K A052196 nonn,word,fini,full
%O A052196 3,1
%A A052196 _Henry Bottomley_, Jan 28 2000
%E A052196 a(11) from _Brian Galebach_, Feb 06 2004
%E A052196 Edited and extended by _Hans Havermann_, Nov 08 2013