A053433 Numbers with distinct digits in alphabetical order (in English).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 17, 20, 30, 32, 40, 41, 42, 43, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 59, 60, 62, 63, 70, 72, 73, 76, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 96, 97, 120, 130, 132, 160, 162, 163, 170, 172, 173, 176

Offset: 1

Author

G. L. Honaker, Jr., Jan 10 2000

Keywords

• easy
• fini
• nonn
• word
• base
• full

Comments

Largest term is 8549176320.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1023
• Eric Weisstein's World of Mathematics, Word Sequence.
• Wikipedia, Zahlen in unterschiedlichen Sprachen
• Wikipedia, List of numbers in various languages

Crossrefs

Subsequence of A053432.

Cf. A247800 (Czech), A247801 (Danish), A247802 (Dutch), A247803 (Finnish), A247804 (French), A247805 (German), A247806 (Hungarian), A247807 (Italian), A247808 (Latin), A247809 (Norwegian), A247810 (Polish), A247807 (Portuguese), A247811 (Russian), A247812 (Slovak), A247813 (Spanish), A247809 (Swedish), A247814 (Turkish).

Programs

Haskell

import Data.IntSet (fromList, deleteFindMin, union)
import qualified Data.IntSet as Set (null)
a053433 n = a053433_list !! (n-1)
a053433_list = 0 : f (fromList [1..9]) where
   f s | Set.null s = []
       | otherwise  = x : f (s' `union`
         fromList (map (+ 10 * x) $ tail $ dropWhile (/= mod x 10) digs))
       where (x, s') = deleteFindMin s
   digs = [8, 5, 4, 9, 1, 7, 6, 3, 2, 0]
-- Reinhard Zumkeller, Oct 05 2014

Python

from itertools import combinations
afull = sorted(int("".join(t)) for d in range(1, 11) for t in combinations("8549176320", d))
print(afull[:65]) # Michael S. Branicky, Aug 17 2022