cp's OEIS Frontend

A050289 Zeroless pandigital numbers: numbers containing the digits 1-9 (each appearing at least once) and no 0's.

%I A050289 #58 Feb 16 2025 08:32:40
%S A050289 123456789,123456798,123456879,123456897,123456978,123456987,
%T A050289 123457689,123457698,123457869,123457896,123457968,123457986,
%U A050289 123458679,123458697,123458769,123458796,123458967,123458976,123459678,123459687,123459768,123459786,123459867,123459876,123465789
%N A050289 Zeroless pandigital numbers: numbers containing the digits 1-9 (each appearing at least once) and no 0's.
%C A050289 The first 9! = 362880 terms of this sequence are permutations of the digits 1-9 with a(9!) = 987654321. - _Jeremy Gardiner_, May 28 2010
%C A050289 First differences are given in A209280 (for the first 9! terms) or in A219664 (for at least as much initial terms). - _M. F. Hasler_, Mar 03 2013
%C A050289 A230959(a(n)) = 0. - _Reinhard Zumkeller_, Nov 02 2013
%C A050289 After the first 9! terms, 8! + 7! = 9*7! of the initial terms are repeated with a leading '1' prefixed, cf. formula. However, a(9!+8!+7!) = 1219...3 is followed by 122...9 and permutations of the last 7 digits, before 12314..9. - _M. F. Hasler_, Jan 08 2020, corrected Aug 11 2022 thanks to a remark from _Michael S. Branicky_
%H A050289 H. Fripertinger, <a href="http://www-ang.kfunigraz.ac.at/~fripert/fga/k1elsn.html">Operate on "9" to display zeroless pandigitals</a>
%H A050289 James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=gaVMrqzb91w">Why 381,654,729 is awesome</a>, Numberphile video (2013).
%H A050289 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PandigitalNumber.html">Pandigital Number</a>
%H A050289 Chai Wah Wu, <a href="https://arxiv.org/abs/2403.20304">Pandigital and penholodigital numbers</a>, arXiv:2403.20304 [math.GM], 2024. See p. 1.
%F A050289 a(n + 9!) = a(n) + 10^9 for 1 <= n <= 8! + 7!. - _M. F. Hasler_, Jan 08 2020, corrected Aug 11 2022
%o A050289 (PARI) apply( {A050289(n)=if(n<=7!*81, fromdigits(Vec(numtoperm(9,n-1)))+(n-1)\9!*10^9, "not yet implemented")}, [1..25]) \\ _M. F. Hasler_, Jan 07 2020, corrected Aug 11 2022
%o A050289 (Python)
%o A050289 from itertools import count, islice, permutations, product
%o A050289 def c(t): return len(set(t)) == 9
%o A050289 def t2i(t): return int("".join(map(str, t)))
%o A050289 def agen():
%o A050289     yield from (t2i(p) for p in permutations(range(1, 10)))
%o A050289     for d in count(10):
%o A050289         yield from (t2i(p) for p in product(range(1, 10), repeat=d) if c(p))
%o A050289 print(list(islice(agen(), 25))) # _Michael S. Branicky_, May 30 2022, updated Aug 05 2022
%Y A050289 Cf. A050290, A133360, A171102.
%K A050289 nonn,base
%O A050289 1,1
%A A050289 _Eric W. Weisstein_
%E A050289 Name clarified by _Michael S. Branicky_, Aug 05 2022