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

Author

Jianing Song, May 17 2022

Keywords

• nonn
• base
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A354049, A354114.

Programs

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

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).