A360443 Smallest integer m > n such that the multiset of nonzero decimal digits of m is exactly the same as the multiset of nonzero decimal digits of n.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 21, 31, 41, 51, 61, 71, 81, 91, 200, 102, 202, 32, 42, 52, 62, 72, 82, 92, 300, 103, 203, 303, 43, 53, 63, 73, 83, 93, 400, 104, 204, 304, 404, 54, 64, 74, 84, 94, 500, 105, 205, 305, 405, 505, 65, 75, 85, 95, 600

Offset: 1

Author

Marc LeBrun and M. F. Hasler, Feb 22 2023

Keywords

• nonn
• easy
• base

Comments

Equivalently: a(n) is the number whose decimal digits are the next larger permutation of those of n, allowing any number of leading zeros.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000
• Wikipedia, Permutation: Generation in lexicographic order, as of Feb. 2023.

Crossrefs

Cf. A057168 (analog for base 2), A354049 (digits of a(n) contain those of n as sub-multiset).

Cf. A009994 (numbers with digits in nondecreasing order: don't appear in this sequence).

Programs

PARI

A360443(n)={forperm(concat(0,digits(n)),p,n||return(fromdigits(Vec(p))); n=0)} \\ M. F. Hasler, Feb 23 2023; similar idea also suggested by Ruud H.G. van Tol.

Python

# From Arthur O'Dwyer, edited by M. F. Hasler, Feb 22 2023
def A360443(n):
    s = '0' + str(n)
    i = next(i for i in range(len(s) - 1, 0, -1) if s[i-1] < s[i])
    tail = s[i-1:]
    j = min((ch, j) for j, ch in enumerate(tail) if s[i-1] < ch)[1]
    s = s[:i-1] + tail[j] + ''.join(sorted(tail[:j] + tail[j+1:]))
    return int(s)
for n in range(1, 100): print(n, A360443(n))