cp's OEIS Frontend

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

%I A008523 #36 Jul 30 2023 05:04:17
%S A008523 0,1,4,5,6,7,9,11,100,101,104,105,106,107,109,111,400,401,404,405,406,
%T A008523 407,409,411,500,501,504,505,506,507,509,511,600,601,604,605,606,607,
%U A008523 609,611,700,701,704,705,706,707,709,711,900,901,904,905,906,907,909,911,1000000,1000001,1000004,1000005
%N A008523 Numbers that do not contain the letter 't'.
%C A008523 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
%H A008523 Reinhard Zumkeller, <a href="/A008523/b008523.txt">Table of n, a(n) for n = 1..1000</a>
%H A008523 Roel and Bas van Dijk, <a href="http://hackage.haskell.org/package/numerals">Numerals package</a>, Hackage (Haskell packages)
%H A008523 <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>
%o A008523 (Haskell)
%o A008523 -- import Data.Maybe (fromJust)
%o A008523 import Data.Text (Text); import qualified Data.Text as T (all)
%o A008523 import Text.Numeral.Grammar.Reified (defaultInflection)
%o A008523 import qualified Text.Numeral.Language.EN as EN  -- see link
%o A008523 a008523 n = a008523_list !! (n-1)
%o A008523 a008523_list = filter (T.all (/= 't') . numeral) [0..] where
%o A008523    numeral :: Integer -> Text
%o A008523    numeral = fromJust . EN.gb_cardinal defaultInflection
%o A008523 -- _Reinhard Zumkeller_, Jan 23 2015
%o A008523 (Python)
%o A008523 from num2words import num2words
%o A008523 from itertools import islice, product
%o A008523 def ok(n): return "t" not in num2words(n)
%o A008523 def agen(): # generator of terms < 10**304
%o A008523     base, pows = [k for k in range(1, 1000) if ok(k)], [1]
%o A008523     yield from ([0] if ok(0) else []) + base
%o A008523     for e in range(3, 304, 3):
%o A008523         if "u" not in num2words(10**e)[4:]:
%o A008523             pows = [10**e] + pows
%o A008523             for t in product([0] + base, repeat=len(pows)):
%o A008523                 if t[0] == 0: continue
%o A008523                 yield sum(t[i]*pows[i] for i in range(len(t)))
%o A008523 print(list(islice(agen(), 60))) # _Michael S. Branicky_, Aug 19 2022
%Y A008523 Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A089590 (ban u).
%Y A008523 Complement of A008522.
%K A008523 nonn,word
%O A008523 1,3
%A A008523 _N. J. A. Sloane_
%E A008523 a(57)-a(60) from _WG Zeist_, Aug 31 2012