cp's OEIS Frontend

A036448 Smallest positive number containing n e's when spelled out in US English.

%I A036448 #38 Dec 06 2020 12:37:16
%S A036448 2,1,3,11,17,111,117,317,1317,3317,11317,17317,111317,117317,317317,
%T A036448 1317317,3317317,11317317,17317317,111317317,117317317,317317317,
%U A036448 1317317317,3317317317,11317317317,17317317317,111317317317,117317317317,317317317317,1317317317317,3317317317317
%N A036448 Smallest positive number containing n e's when spelled out in US English.
%C A036448 From _Michael S. Branicky_, Oct 24 2020: (Start)
%C A036448 "US English" connotes that no "and" is used ("one hundred one") and, importantly here, that the names of large numbers follow the "American system" (Weisstein link), also known as the short scale (Wikipedia link). The previous a(8) and a(9) were based on "eleven hundred and seventeen" and "seventeen hundred and seventeen", which are less common written forms (Wikipedia English numbers link). To make the sequence precise, the common written form is adopted ("one thousand one hundred seventeen"; Wilson link; A000052 Example). Thus, a(n) is the least m such that A085513(m)=n.
%C A036448 The sequence follows the pattern of 1(317)^n, 3(317)^n, 11(317)^n, 17(317)^n, 111(317)^n, 117(317)^n, 317(317)^n for n = 0 through 7 and whenever the largest named power has no "e". a(50) > 10^21 = "one sextillion" which is the first power name that has an "e", breaking the pattern. In that case, a(50) = 1117(317)^6 and a(51) = 1(317)^7. Whenever the largest power has 1 "e" it follows this pattern. If it has m>1 "e"'s, the first block of three is shifted lower to a(7-m). See Wikipedia link for Names of large numbers for power names.
%C A036448 (End)
%D A036448 Rodolfo Marcelo Kurchan, Problem 1882, Another Number Sequence, Journal of Recreational Mathematics, vol. 23, number 2, p. 141.
%H A036448 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LargeNumber.html">Large Number</a>
%H A036448 Wikipedia, <a href="https://en.wikipedia.org/wiki/English_numerals">English numerals</a>
%H A036448 Wikipedia, <a href="https://en.wikipedia.org/wiki/Names_of_large_numbers">Names of Large Numbers</a>
%H A036448 Robert G. Wilson v, <a href="https://oeis.org/A001477/a001477.txt">American English names for the numbers from 0 to 100999 without spaces or hyphens</a>
%e A036448 One has 1 e.
%e A036448 Three has 2 e's.
%o A036448 (Python)
%o A036448 from num2words import num2words
%o A036448 def A036448(n):
%o A036448     i = 1
%o A036448     while num2words(i).count("e")!=n:
%o A036448         i += 1
%o A036448     return i
%o A036448 print([A036448(n) for n in range(1,12)]) # _Michael S. Branicky_, Oct 23 2020
%Y A036448 Cf. A000027, A000052, A001477, A005589, A006933, A037196, A085513.
%K A036448 nonn,word
%O A036448 0,1
%A A036448 _Rodolfo Kurchan_
%E A036448 a(8)-a(9) changed and a(11)-a(30) added by _Michael S. Branicky_, Oct 23 2020
%E A036448 a(0)=2 inserted by _Sean A. Irvine_, Nov 02 2020