cp's OEIS Frontend

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

A number m is k-persistent iff all of {m, 2m,..., km} are pandigital (in the sense of A171102).

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).

A number n is k-persistent iff all of {n, 2*n, ..., k*n} are pandigital (in the sense of A171102).

a(9) is 0 because any 9-persistent number is also 10-persistent. Indeed, if n is pandigital, 10*n is pandigital as well.

In the same way, a(10m-1)=0 for all m>0 since if kn is pandigital for all k=1,...,10m-1, then mn is pandigital and so is 10mn. - M. F. Hasler, Jan 10 2012

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).