A089590 Uban numbers (the letter u is banned from the English name of the number).

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99

Offset: 1

Author

Eric W. Weisstein, Nov 09 2003

Keywords

• nonn
• easy
• word

Comments

The sequence of uban numbers first differs from A052406 (the numbers not containing the digit 4) at the term 40 (forty), which is a uban number but is not 4-less.

Links

• Daniel Arribas and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 (first 89 terms from Daniel Arribas)
• Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
• Eric Weisstein's World of Mathematics, Uban Number
• Index entries for sequences related to number of letters in n

Crossrefs

Cf. A052406.

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A008523 (ban t).

Programs

Haskell

import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (all)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a089590 n = a089590_list !! (n-1)
a089590_list = filter (T.all (/= 'u') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

Python

from num2words import num2words
from itertools import islice, product
def ok(n): return "u" not in num2words(n)
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if "u" not in num2words(10**e)[4:]:
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 100))) # Michael S. Branicky, Aug 19 2022

Extensions

a(1) = 0 prepended by Reinhard Zumkeller, Jan 23 2015