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

1,3

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

Prog

(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

Crossrefs

Cf. A052406.

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

Sequence in context: A242410 A258022 A333638 * A052406 A022306 A183298

Adjacent sequences: A089587 A089588 A089589 * A089591 A089592 A089593

Keyword

nonn,easy,word

Author

Eric W. Weisstein, Nov 09 2003

Extensions

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

Status

approved