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

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

0,1

Comments

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.

Links

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

Formula

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).

Example

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.

Prog

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

Crossrefs

Cf. A354049, A354114.

Sequence in context: A369604 A063660 A354049 * A354114 A175220 A272479

Adjacent sequences: A354110 A354111 A354112 * A354114 A354115 A354116

Keyword

nonn,base,easy

Author

Jianing Song, May 17 2022

Status

approved