A074157 Smallest multiple of n which uses no digits of n, or 0 if no such number exists.

2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 22, 36, 26, 28, 30, 32, 34, 36, 38, 0, 63, 44, 46, 96, 100, 78, 54, 56, 58, 0, 62, 64, 66, 68, 70, 72, 111, 76, 78, 0, 82, 168, 86, 88, 90, 92, 188, 96, 588, 0, 204, 104, 106, 108, 110, 112, 114, 116, 118, 0, 244, 310, 189, 128

Offset

1,1

Comments

For numbers n of the form 10k, of the form 10k+5 with a zero somewhere, and those using all 10 digits, a(n) = 0.

Are there numbers using 8 of the 9 nonzero digits for which a(n) is nonzero? If so, what is the smallest such number?

All such numbers have a(n) nonzero since a candidate value for a(n) is d*A052983(n) where d is the nonzero digit not in n. - Gonzalo Martínez, Dec 12 2024

Links

Michel Marcus, Table of n, a(n) for n = 1..1000

Prog

(PARI) a(n) = if(!(n%10), return(0)); my(dn = Set(digits(n))); if(#dn==10 || (#dn==9 && dn[1]==1), return(0)); if(!(n%5) && !dn[1], return(0)); if(!(n%2), my(v=setminus([0, 2, 4, 6, 8], dn)); if(!#v || (#v==1 && #dn==9 && valuation(n, 2)>valuation(v[1], 2)) || (v==[2, 6] && #dn==8 && valuation(n, 2)>1), return(0))); forstep(m=2*n, oo, n, if(!#setintersect(Set(digits(m)), dn), return(m))); \\ Michel Marcus, Aug 04 2017 (Corrected by Jinyuan Wang, Jun 15 2025)

Crossrefs

Cf. A052983, A076924, A378865.

Sequence in context: A069816 A088116 A100817 * A076309 A088133 A115299

Adjacent sequences: A074154 A074155 A074156 * A074158 A074159 A074160

Keyword

nonn,base

Author

Amarnath Murthy, Aug 29 2002

Extensions

a(24) and a(49) corrected by Michel Marcus, Aug 04 2017

Status

approved