A000052 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.

8, 5, 4, 9, 1, 7, 6, 3, 2, 0, 18, 80, 88, 85, 84, 89, 81, 87, 86, 83, 82, 11, 15, 50, 58, 55, 54, 59, 51, 57, 56, 53, 52, 40, 48, 45, 44, 49, 41, 47, 46, 43, 42, 14, 19, 90, 98, 95, 94, 99, 91, 97, 96, 93, 92, 17, 70, 78, 75, 74, 79, 71, 77, 76, 73, 72

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• word

Comments

This sequence uses standard US English names for numbers. - Daniel Forgues, May 11 2016

For example, standard US English writes out the number 101 as "one hundred one", whereas standard UK English writes it out as "one hundred and one" (see Links). - Jon E. Schoenfield, Dec 25 2016

Alphabetical order is with spaces removed/disregarded, else, as a first example, a(1003)=8018 ("eight thousand eighteen") would follow a(1004)=8800 ("eight thousand eight hundred") among others. - Michael S. Branicky, Aug 05 2021

Examples

			eight, five, four, nine, one, seven, six, three, two, zero, eighteen, etc.
Examples of spelling convention used for values above 99:
400: "four hundred"
726: "seven hundred twenty-six"
1992: "one thousand nine hundred ninety-two"
2202: "two thousand two hundred two"
101001: "one hundred one thousand one"
726726: "seven hundred twenty-six thousand seven hundred twenty-six"
101000001: "one hundred one million one"
		

Links

• Table of n, a(n) for n = 1..10000
• Wikipedia, 101st United States Congress
• Wiktionary, one hundred one (US)
• Wiktionary, one hundred and one (UK)

Crossrefs

Cf. A001058.

Programs

Maple

V:= [[$0..9],[$10..99],[$100..999]]:
seq(op(V[i][sort(map(convert,V[i],english,'And'),
output=permutation)]),i=1..3); # Robert Israel, Jun 17 2016

Mathematica

Flatten@Join[{8, 5, 4, 9, 1, 7, 6, 3, 2, 0}, SortBy[Range[10^#, 10^(# + 1) - 1], StringReplace[IntegerName[#, "Words"], "," -> ""] &] & /@ Range[3]] (* Davin Park, Dec 25 2016 *)

Python

from num2words import num2words
def n2w(n):
  return num2words(n).replace(" and", "").replace(",", "").replace(" ", "")
def agen(maxdigits):
  for d in range(1, maxdigits+1):
    yield from sorted(range(10**(d-1)-(d==1), 10**d), key=lambda x: n2w(x))
print([an for an in agen(2)]) # Michael S. Branicky, Aug 05 2021

Extensions

Corrected by Davin Park, Dec 25 2016