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

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))
            if m > n: return m
print([a(n) for n in range(75)]) # Michael S. Branicky, Oct 29 2022

Crossrefs

Cf. A002275, A050278, A050289, A171102.

Cf. A358098 (similar, with largest integer m < n).

Sequence in context: A134817 A067581 A099469 * A039112 A160015 A276392

Adjacent sequences: A358094 A358095 A358096 * A358098 A358099 A358100

Keyword

nonn,base

Author

Bernard Schott, Oct 29 2022

Status

approved