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A171102 Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once. 44

%I

%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

%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>

%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 this is faster than other possibilities involving Set(),Vec(),eval() */ \\ _M. F. Hasler_, Jan 10 2012

%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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Last modified August 21 17:55 EDT 2017. Contains 290893 sequences.