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

1,3

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.

Links

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

Formula

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

a(A050289(n))=0.

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A050289, A050278, A171102.

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

Sequence in context: A249121 A289410 A225673 * A257779 A328865 A329623

Adjacent sequences: A358095 A358096 A358097 * A358099 A358100 A358101

Keyword

nonn,base

Author

Bernard Schott, Oct 29 2022

Status

approved