A053432 Numbers with digits in alphabetical order (in English).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 20, 22, 30, 32, 33, 40, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 62, 63, 66, 70, 72, 73, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 97, 99, 100

Offset: 1

Author

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

Keywords

• nonn
• base
• word
• easy

Comments

a(142447) = A053433(1023) = 8549176320 is the greatest term not containing any repeating digits. - Reinhard Zumkeller, Oct 05 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Word Sequence
• Wikipedia, Zahlen in unterschiedlichen Sprachen
• Wikipedia, List of numbers in various languages

Crossrefs

Cf. A247750 (Czech), A247751 (Danish), A247752 (Dutch), A247753 (Finnish), A247754 (French), A247755 (German), A247756 (Hungarian), A247757 (Italian), A247758 (Latin), A247759 (Norwegian), A247760 (Polish), A247757 (Portuguese), A247761 (Russian), A247762 (Slovak), A161390 (Spanish), A247759 (Swedish), A247764 (Turkish).

Programs

Haskell

import Data.IntSet (fromList, deleteFindMin, union)
a053432 n = a053432_list !! (n-1)
a053432_list = 0 : f (fromList [1..9]) where
   f s = x : f (s' `union`
         fromList (map (+ 10 * x) $ 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 count, islice, combinations_with_replacement as cwr
def agen(): # generator of terms
    for d in count(1):
        out = sorted(int("".join(t)) for t in cwr("8549176320", d))
        yield from out[1-int(d==1):] # remove extra 0's
print(list(islice(agen(), 65))) # Michael S. Branicky, Aug 17 2022