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

1,3

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

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
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

Crossrefs

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

Sequence in context: A095033 A010399 A215046 * A047568 A139453 A010391

Adjacent sequences: A008520 A008521 A008522 * A008524 A008525 A008526

Keyword

nonn,word

Author

N. J. A. Sloane

Extensions

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

Status

approved