A358097 - OEIS

A358097

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

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 20, 30, 20, 20, 20, 20, 20, 20, 20, 31, 30, 30, 40, 30, 30, 30, 30, 30, 30, 41, 40, 40, 40, 50, 40, 40, 40, 40, 40, 51, 50, 50, 50, 50, 60, 50, 50, 50, 50, 61, 60, 60, 60, 60, 60, 70, 60, 60, 60, 71, 70, 70, 70, 70, 70, 70, 80, 70, 70, 81, 80, 80, 80, 80

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OFFSET

0,2

COMMENTS

When n is pandigital with or without 0 (A050278, A050289, A171102), m does not exist, so a(n) = -1; see examples for smallest pandigital cases.

LINKS

Michel Marcus, Table of n, a(n) for n = 0..10000

FORMULA

a(10^n-k) = 10^n when n >= 2 and 1 <= k <= 8.

a(10^n) = 2 * A002275(n+1), when n >= 1.

EXAMPLE

a(10) = 22; a(11) = 20; a(12) = 30.

a(123456789) = -1; a(1234567890) = -1.

MATHEMATICA

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

PROG

(PARI) isfull(d) = my(dd=setminus([0..9], d)); (dd==[]) || (dd==[0]);

a(n) = my(d=Set(digits(n))); if (isfull(d), -1, my(k=n+1); while (#setintersect(Set(digits(k)), d), k++); k); \\ Michel Marcus, Oct 29 2022

(Python)

from itertools import count, product

def a(n):

s = str(n)

r = sorted(set("1234567890") - set(s))

if len(r) == 0 or r == ["0"]: return -1

for d in count(len(s)):

for p in product(r, repeat=d):

m = int("".join(p))