cp's OEIS Frontend

A129774 Main diagonal of table of length of English names of numbers.

%I A129774 #21 Dec 26 2020 08:14:49
%S A129774 1,5,8,30,0,42,36,47,79,3000000,606,502,301,305,420,218,181,176,233,
%T A129774 367,578,2101,2105,1607,1540,1616,1311,1232,1235,1298,1423,1787,3348,
%U A129774 3793,11375,13358,13823,17577,23339,23833,37777,101398,103384,103875,111478,113394
%N A129774 Main diagonal of table of length of English names of numbers.
%C A129774 a(n) is the n-th smallest positive integer with the property that, when spelled out in American English, has n+2 letters (or 0 if fewer than n such numbers exists).
%C A129774 The sequence is labeled "finite" because there is no widely accepted naming convention for arbitrarily large numbers.
%C A129774 The table {and length of each row} begins:
%C A129774 3..|.1..2..6.10.........{4}
%C A129774 4..|.4..5..9............{3}
%C A129774 5..|.3..7..8.40.50.60...{6}
%C A129774 6..|11.12.20.30.80.90...{6}
%C A129774 7..|15.16.70............{3}
%C A129774 8..|13.14.18.19.41.42.46.51.52.56.61.62.66.{13}
%C A129774 From _Michael S. Branicky_, Jul 13 2020: (Start)
%C A129774 9..|17.21.22.26.31.32.36.44.45.49.54.55.59.64.65.69.81.82.86.91.92.96.{22}
%C A129774 10.|24.25.29.34.35.39.43.47.48.53.57.58.63.67.68.71.72.76.84.85.89.94.95.99...
%C A129774 11.|23.27.28.33.37.38.74.75.79.83.87.88.93.97.98.400.500.900.1000.2000.6000.10000.400000.5000000...
%C A129774 12.|73.77.78.300.700.800.4000.5000.9000.3000000.7000000.8000000.40000000.50000000.60000000...
%C A129774 13.|101.102.106.110.201.202.206.210.601.602.606.610.3000.700.8000.40000.50000.60000.1000001.1000002...
%C A129774 14.|104.105.109.204.205.209.401.402.406.410.501.502.506.510.604.605.609.901.902.906.910.1001.1002.1006...
%C A129774 15.|103.107.108.140.150.160.203.207.208.240.250.260.301.302.306.310.404.405.409.504.505.509.603.607...
%C A129774 16.|111.112.120.130.180.190.211.212.220.230.280.290.304.305.309.403.407.408.440.450.460.503.507.508...
%C A129774 17.|115.116.170.215.216.270.303.307.308.340.350.360.411.412.420.430.480.490.511.512.520.530.580.590...
%C A129774 18.|113.114.118.119.141.142.146.151.152.156.161.162.166.213.214.218.219.241.242.246.251.252.256.261...
%C A129774 19.|117.121.122.126.131.132.136.144.145.149.154.155.159.164.165.169.181.182.186.191.192.196.217.221...
%C A129774 20.|124.125.129.134.135.139.143.147.148.153.157.158.163.167.168.171.172.176.184.185.189.194.195.199...
%C A129774 21.|123.127.128.133.137.138.174.175.179.183.187.188.193.197.198.223.227.228.233.237.238.274.275.279...
%C A129774 22.|173.177.178.273.277.278.324.325.329.334.335.339.343.347.348.353.357.358.363.367.368.371.372.376...
%C A129774 23.|323.327.328.333.337.338.374.375.379.383.387.388.393.397.398.473.477.478.573.577.578.723.727.728..(End)
%F A129774 a(n) = A(n+2,n) where A(k,n) = n-th positive integer requiring exactly k letters (not including "and" or hyphens) in its English name, or 0 if no such integer.
%e A129774 a(1) = 1 because "one" is the first positive integer with 3 letters in its name.
%e A129774 a(2) = 5 because "five" is the second positive integer with 4 letters.
%e A129774 a(3) = 8 because "eight" is the third positive integer with 5 letters.
%e A129774 a(4) = 30 because "thirty" is the fourth positive integer with 6 letters.
%e A129774 a(5) = 0 because there are only three 7-letter positive integers: {15, 16, 70}.
%o A129774 (Python)
%o A129774 def A129774(n):
%o A129774   i, found, limit = 0, 0, 10**2
%o A129774   while found < n-2 and i < limit:
%o A129774     i += 1
%o A129774     found += 1*(A005589(i)==n)
%o A129774   return i*(i < limit)
%o A129774 print([A129774(i) for i in range(3,12)]) # _Michael S. Branicky_, Jul 13 2020
%Y A129774 Cf. A000916, A001166, A014388, A045494, A045495, A005589, A080777, A084390.
%K A129774 easy,fini,nonn,word,less
%O A129774 1,2
%A A129774 _Jonathan Vos Post_, May 17 2007, May 21 2007
%E A129774 Corrected and edited by _Danny Rorabaugh_, May 13 2016
%E A129774 Corrected terms a(10)-a(18) and table in comments from 9; added terms from a(20) - _Michael S. Branicky_, Jul 13 2020