OFFSET
1,1
COMMENTS
This is the infinite version. See A050278 for the finite version.
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
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]
A230959(a(n)) = 0. - Reinhard Zumkeller, Nov 02 2013
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
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
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1000 . [From Robert G. Wilson v, May 30 2010]
Eric Weisstein's World of Mathematics, Pandigital Number.
Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
FORMULA
a(n) = 1011111111 + A178478(n) for n = 1,...,8!. - M. F. Hasler, Jan 10 2012
MATHEMATICA
Take[ Select[ FromDigits@# & /@ Permutations[ Range[0, 9], {10}], # > 10^9 &], 20] (* Robert G. Wilson v, May 30 2010 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Sep 25 2010
STATUS
approved