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

Author

Amarnath Murthy, Aug 29 2002

Keywords

• nonn
• base

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

Crossrefs

Cf. A052983, A076924, A378865.

Programs

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)

Extensions

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