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

1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976

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

Subsequence of A134336 and of A178403; A178401(a(n))>0. - Reinhard Zumkeller, May 27 2010

Smallest prime factors: A178775(n) = A020639(a(n)). - Reinhard Zumkeller, Jun 11 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

A171102(n) = A050278(n) for n <= 9*9!.

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
(PARI) A171102=A050278 /*** valid for n <= 9*9! ***/ \\ M. F. Hasler, Jan 10 2012

Crossrefs

Cf. A050278, A050288, A050289.

Cf. A051264, A051018, A051019, A051020.

Subsequence of A253172.

Sequence in context: A204045 A061604 A302096 * A050278 A051018 A020667

Adjacent sequences: A171099 A171100 A171101 * A171103 A171104 A171105

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 25 2010

Status

approved