A354049 -id:A354049 - cp's OEIS frontend

A354114 The smallest number that contains all the digits of n as a substring but does not equal n.

10, 10, 12, 13, 14, 15, 16, 17, 18, 19, 100, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset: 0

Jianing Song, May 17 2022

Suppose that n > 0 is a k-digit number. If 10^(k-1) <= a(n) <= (10^k-1)/9, then a(n) is obtained by placing a 0 after n; otherwise a(n) is obtained by placing a 1 before n.

			The smallest number not equal to 111 containing the substring "111" in its decimal expansion is 1110, so a(111) = 1110.
The smallest number not equal to 112 containing the substring "112" in its decimal expansion is 1112, so a(112) = 1112.

Jianing Song, Table of n, a(n) for n = 0..10000

Cf. A354049, A354113.

a(n) = if(n==0, 10, my(k=logint(n,10)); if(n<=10^(k+1)\9, 10*n, n+10^(k+1)))

def a(n):
    if n == 0: return 10
    s = str(n)
    return n*10 if s <= "1"*len(s) else int("1"+s)
print([a(n) for n in range(54)]) # Michael S. Branicky, May 17 2022

If 10^k <= n <= (10^(k+1)-1)/9, a(n) = 10*n; if (10^(k+1)-1)/9 <= n < 10^(k+1), a(n) = n + 10^(k+1).

A354113 The smallest number that contains all the digits of n in order but does not equal n.

Original entry on oeis.org

10, 10, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset: 0

Jianing Song, May 17 2022

If n begins with 1, then a(n) is obtained by inserting a 0 after it; otherwise a(n) is obtained by placing a 1 before n.

			The smallest number not equal to 19 containing the digits 1 and 9 in that order is 109, so a(19) = 109.
The smallest number not equal to 22 containing two 2's is 122, so a(22) = 122.

Jianing Song, Table of n, a(n) for n = 0..10000

Cf. A354049, A354114.

a(n) = if(n==0, 10, my(k=logint(n,10)); if(n<2*10^k, n+9*10^k, n+10^(k+1)))

def a(n):
    if n == 0: return 10
    s = str(n)
    return int(s[0]+"0"+s[1:]) if s[0] == "1" else int("1"+s)
print([a(n) for n in range(54)]) # Michael S. Branicky, May 17 2022

If 10^k <= n < 2*10^k, a(n) = n + 9*10^k; if 2*10^k <= n < 10^(k+1), a(n) = n + 10^(k+1).

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.

Original entry on oeis.org

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

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

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

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

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).

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.

# 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))

cp's OEIS Frontend

A354114 The smallest number that contains all the digits of n as a substring but does not equal n.

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A354113 The smallest number that contains all the digits of n in order but does not equal n.

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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.

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Python