A008523 Numbers that do not contain the letter 't'.

0, 1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, 407, 409, 411, 500, 501, 504, 505, 506, 507, 509, 511, 600, 601, 604, 605, 606, 607, 609, 611, 700, 701, 704, 705, 706, 707, 709, 711, 900, 901, 904, 905, 906, 907, 909, 911, 1000000, 1000001, 1000004, 1000005

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• word

Comments

See also A006933, the eban numbers (numbers not containing 'e'), and A089589 (the iban numbers). This sequence might correspondingly be called the "tban" numbers. - WG Zeist, Aug 31 2012

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
• Index entries for sequences related to number of letters in n

Crossrefs

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A089590 (ban u).

Complement of A008522.

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
a008523 n = a008523_list !! (n-1)
a008523_list = filter (T.all (/= 't') . 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 "t" 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(), 60))) # Michael S. Branicky, Aug 19 2022

Extensions

a(57)-a(60) from WG Zeist, Aug 31 2012