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%I #54 Apr 04 2024 10:13:39
%S 1023456789,1023456798,1023456879,1023456897,1023456978,1023456987,
%T 1023457689,1023457698,1023457869,1023457896,1023457968,1023457986,
%U 1023458679,1023458697,1023458769,1023458796,1023458967,1023458976
%N Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once.
%C This is the infinite version. See A050278 for the finite version.
%C The first 9*9!=3265920 terms of this sequence are permutations of the digits 0-9 with a(9*9!)=9876543210 (see Version 1, A050278). - _Jeremy Gardiner_, May 29 2010
%C Subsequence of A134336 and of A178403; A178401(a(n))>0. - _Reinhard Zumkeller_, May 27 2010
%C Smallest prime factors: A178775(n) = A020639(a(n)). - _Reinhard Zumkeller_, Jun 11 2010
%C A178788(a(n)) = 1, for n <= 9*9!, else A178788(a(n)) = 0. - _Reinhard Zumkeller_, Jun 30 2010 [corrected by _Hieronymus Fischer_, Feb 02 2013]
%C A230959(a(n)) = 0. - _Reinhard Zumkeller_, Nov 02 2013
%C The first term of the sequence absent in A050278 is a(3265921) = 10123456789. Also, the first prime is a(3306373) = 10123457689 = A050288(1). - _Zak Seidov_, Sep 23 2015
%C Almost all numbers are in this sequence, in the sense that it has asymptotic density equal to 1. Indeed, the fraction of n-digit numbers which don't have a given digit d is roughly 0.9^n (not exactly because the first digit is chosen among {1..9}) which tends to zero as n -> oo. - _M. F. Hasler_, Jan 05 2020
%H Robert G. Wilson v, <a href="/A171102/b171102.txt">Table of n, a(n) for n = 1..1000 </a>. [From _Robert G. Wilson v_, May 30 2010]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PandigitalNumber.html">Pandigital Number.</a>
%H 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 a(n) = 1011111111 + A178478(n) for n = 1,...,8!. - _M. F. Hasler_, Jan 10 2012
%F A171102(n) = A050278(n) for n <= 9*9!.
%t Take[ Select[ FromDigits@# & /@ Permutations[ Range[0, 9], {10}], # > 10^9 &], 20] (* _Robert G. Wilson v_, May 30 2010 *)
%o (PARI) is_A171102(n)=9<#vecsort(Vecsmall(Str(n)),,8) /* assuming that n is a nonnegative integer. In PARI/GP V.2.4 - 2.9 this is faster than other possibilities involving Set(),Vec(),eval() or digits() */ \\ _M. F. Hasler_, Jan 10 2012, Sep 19 2017
%o (PARI) A171102=A050278 /*** valid for n <= 9*9! ***/ \\ _M. F. Hasler_, Jan 10 2012
%Y Cf. A050278, A050288, A050289.
%Y Cf. A051264, A051018, A051019, A051020.
%Y Subsequence of A253172.
%K nonn,base
%O 1,1
%A _N. J. A. Sloane_, Sep 25 2010
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