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

1,1

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.

Prog

(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(100): print(n, A360443(n))

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).

Sequence in context: A370400 A156819 A139079 * A209932 A011540 A098394

Adjacent sequences: A360440 A360441 A360442 * A360444 A360445 A360446

Keyword

nonn,easy,base

Author

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

Status

approved