A045495 -id:A045495 - cp's OEIS frontend

A001166 Smallest natural number requiring n letters in English.

1, 4, 3, 11, 15, 13, 17, 24, 23, 73, 3000, 11000, 15000, 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, 101123, 101173, 101323, 101373, 103323, 103373, 111373, 113323, 113373, 117373

Offset: 3

N. J. A. Sloane

In this version 101 is written "one hundred and one", etc.

			For n = 6, the smallest natural number requiring 6 letters in English is "eleven." - _Julia Carrigan_, Jan 19 2024

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Sean A. Irvine, Illustration of terms a(3) through a(75)

Cf. A000916, A014388, A045494, A045495, A080777.

Corrected and extended by Henry Bottomley, Jan 28 2000
Further corrected and extended by Brian Galebach, Feb 06 2004
Further corrected and illustration of terms by Sean A. Irvine, Mar 12 2012

A045494 Smallest positive integer requiring at least n letters (not including hyphens) when spelled out in English.

Original entry on oeis.org

1, 1, 1, 3, 3, 11, 13, 13, 17, 23, 23, 73, 101, 103, 103, 111, 113, 113, 117, 123, 123, 173, 323, 373, 1103, 1103, 1111, 1113, 1113, 1117, 1123, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323

Offset: 1

Brian Galebach

Assumes British definition of billion, trillion. Also assumes no 'and' is used to spell integers.

Cf. A000916, A001166, A014388, A045494, A045495, A045495, A167509.

Added "at least" in definition M. F. Hasler, Nov 18 2009

A014388 a(2n-1) = n+2, a(2n) = smallest number requiring n+2 letters in English.

Original entry on oeis.org

3, 1, 4, 4, 5, 3, 6, 11, 7, 15, 8, 13, 9, 17, 10, 24, 11, 23, 12, 73, 13, 3000, 14, 11000, 15, 15000, 16, 101, 17, 104, 18, 103, 19, 111, 20, 115, 21, 113, 22, 117, 23, 124, 24, 123, 25, 173, 26, 323, 27, 373, 28, 1104, 29, 1103, 30, 1111, 31

Offset: 1

Jacques Haubrich (jhaubrich(AT)freeler.nl)

Uses number forms containing "and"; that is, "one hundred and one" rather than "one hundred one". - Sean A. Irvine, Oct 20 2018

Cf. A000916, A001166, A014388, A045494, A045495.

More terms from Sean A. Irvine, Oct 20 2018

A000916 a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English.

Original entry on oeis.org

1, 3, 4, 4, 3, 5, 11, 6, 15, 7, 13, 8, 17, 9, 24, 10, 23, 11, 73, 12, 3000, 13, 11000, 14, 15000, 15, 101, 16, 104, 17, 103, 18, 111, 19, 115, 20, 113, 21, 117, 22, 124, 23, 123, 24, 173, 25, 323, 26, 373, 27, 1104, 28, 1103, 29, 1111, 30

Offset: 1

Jacques Haubrich (jhaubrich(AT)freeler.nl)

Requires presence of "and" at appropriate place, e.g. "one hundred and one". - Sean A. Irvine, Aug 29 2011.

Cf. A001166, A014388, A045494, A045495.

More terms from Sean A. Irvine, Aug 28 2011

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

Original entry on oeis.org

1, 5, 8, 30, 0, 42, 36, 47, 79, 3000000, 606, 502, 301, 305, 420, 218, 181, 176, 233, 367, 578, 2101, 2105, 1607, 1540, 1616, 1311, 1232, 1235, 1298, 1423, 1787, 3348, 3793, 11375, 13358, 13823, 17577, 23339, 23833, 37777, 101398, 103384, 103875, 111478, 113394

Offset: 1

Jonathan Vos Post, May 17 2007, May 21 2007

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).
The sequence is labeled "finite" because there is no widely accepted naming convention for arbitrarily large numbers.
The table {and length of each row} begins:
.|.1..2..6.10.........{4}
.|.4..5..9............{3}
.|.3..7..8.40.50.60...{6}
.|11.12.20.30.80.90...{6}
.|15.16.70............{3}
.|13.14.18.19.41.42.46.51.52.56.61.62.66.{13}
From Michael S. Branicky, Jul 13 2020: (Start)
.|17.21.22.26.31.32.36.44.45.49.54.55.59.64.65.69.81.82.86.91.92.96.{22}
|24.25.29.34.35.39.43.47.48.53.57.58.63.67.68.71.72.76.84.85.89.94.95.99...
|23.27.28.33.37.38.74.75.79.83.87.88.93.97.98.400.500.900.1000.2000.6000.10000.400000.5000000...
|73.77.78.300.700.800.4000.5000.9000.3000000.7000000.8000000.40000000.50000000.60000000...
|101.102.106.110.201.202.206.210.601.602.606.610.3000.700.8000.40000.50000.60000.1000001.1000002...
|104.105.109.204.205.209.401.402.406.410.501.502.506.510.604.605.609.901.902.906.910.1001.1002.1006...
|103.107.108.140.150.160.203.207.208.240.250.260.301.302.306.310.404.405.409.504.505.509.603.607...
|111.112.120.130.180.190.211.212.220.230.280.290.304.305.309.403.407.408.440.450.460.503.507.508...
|115.116.170.215.216.270.303.307.308.340.350.360.411.412.420.430.480.490.511.512.520.530.580.590...
|113.114.118.119.141.142.146.151.152.156.161.162.166.213.214.218.219.241.242.246.251.252.256.261...
|117.121.122.126.131.132.136.144.145.149.154.155.159.164.165.169.181.182.186.191.192.196.217.221...
|124.125.129.134.135.139.143.147.148.153.157.158.163.167.168.171.172.176.184.185.189.194.195.199...
|123.127.128.133.137.138.174.175.179.183.187.188.193.197.198.223.227.228.233.237.238.274.275.279...
|173.177.178.273.277.278.324.325.329.334.335.339.343.347.348.353.357.358.363.367.368.371.372.376...
|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)

			a(1) = 1 because "one" is the first positive integer with 3 letters in its name.
a(2) = 5 because "five" is the second positive integer with 4 letters.
a(3) = 8 because "eight" is the third positive integer with 5 letters.
a(4) = 30 because "thirty" is the fourth positive integer with 6 letters.
a(5) = 0 because there are only three 7-letter positive integers: {15, 16, 70}.

Cf. A000916, A001166, A014388, A045494, A045495, A005589, A080777, A084390.

def A129774(n):
  i, found, limit = 0, 0, 10**2
  while found < n-2 and i < limit:
    i += 1
    found += 1*(A005589(i)==n)
  return i*(i < limit)
print([A129774(i) for i in range(3,12)]) # Michael S. Branicky, Jul 13 2020

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.

Corrected and edited by Danny Rorabaugh, May 13 2016

Corrected terms a(10)-a(18) and table in comments from 9; added terms from a(20) - Michael S. Branicky, Jul 13 2020

cp's OEIS Frontend

A001166 Smallest natural number requiring n letters in English.

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A045494 Smallest positive integer requiring at least n letters (not including hyphens) when spelled out in English.

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A014388 a(2n-1) = n+2, a(2n) = smallest number requiring n+2 letters in English.

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A000916 a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English.

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

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