A358098 a(n) is the largest integer m < n such that m and n have no common digit, or -1 when such integer m does not exist.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 19, 9, 19, 19, 19, 19, 19, 19, 19, 18, 29, 29, 19, 29, 29, 29, 29, 29, 29, 28, 39, 39, 39, 29, 39, 39, 39, 39, 39, 38, 49, 49, 49, 49, 39, 49, 49, 49, 49, 48, 59, 59, 59, 59, 59, 49, 59, 59, 59, 58, 69, 69, 69, 69, 69, 69, 59, 69, 69, 68, 79

Offset: 1

Author

Bernard Schott, Oct 29 2022

Keywords

• nonn
• base

Comments

Note that only when n is pandigital with 0 (A050278, A171102), such m does not exist and a(n) = -1; see examples for smallest pandigital cases.

Examples

			a(19) = 8, a(20) = 19; a(21) = 9.
a(123456789) = 0; a(1234567890) = -1.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050289, A050278, A171102.

Cf. A358097 (similar, with smallest integer m > n).

Programs

Mathematica

a[n_] := Module[{d = Complement[Range[0, 9], IntegerDigits[n]], m = n - 1}, If[d == {} || d == {0}, -1, While[m >= 0 && ! AllTrue[IntegerDigits[m], MemberQ[d, #] &], m--]; m]]; Array[a, 100] (* Amiram Eldar, Oct 29 2022 *)

PARI

a(n) = my(d=Set(digits(n))); forstep (m=n-1, 0, -1, if (!#setintersect(d, Set(digits(m))), return(m))); return(-1); \\ Michel Marcus, Oct 30 2022

Python

from itertools import product
def a(n):
    s = str(n)
    r = sorted(set("1234567890") - set(s), reverse=True)
    if len(r) == 0: return -1
    if r == ["0"]: return 0
    for d in range(len(s), 0, -1):
        for p in product(r, repeat=d):
            m = int("".join(p))
            if m < n: return m
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Oct 29 2022

Formula

a(10^n) = 10^n - 1 for n >= 0.

a(A050289(n))=0.